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S.chand Class 8 Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 G

Exercise 6 G

Factorise:

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Question 1

$4 x^{2}+5 x+1$

Sol :

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Question 2

$2 x^{2}+11 x+14$

Sol :

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Question 3

$2 x^{2}+11 x+12$

Sol :

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Question 4

$3 x^{2}+13 x+4$

Sol :

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Question 5

$2 x^{2}-5 x-12$

Sol :

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Question 6

$4 x^{2}+8 x-5$

Sol :

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Question 7

$13 x^{2}+37 x-6$

Sol :

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Question 8

$40 n^{2}+n-6$

Sol :

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Question 9

$4 z^{2}-16 z+15$

Sol :

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Question 10

$6-9 c-27 c^{2}$

Sol :

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Question 11

$1-t-6 t^{2}$

Sol :

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Question 12

$2 a^{2}+7 a b-15 b^{2}$

Sol :

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Question 13

$4 x^{2}+24 x+20$

Sol :

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Question 14

$12 a^{2}+2 a-4$

Sol :

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Question 15

$12 m^{3}+6 m^{2}-6 m$

Sol :

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Question 16

$6 x^{5}-22 x^{3}-8 x$

Sol :

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Question 17

$6 z^{6}-21 z^{4}-12 z^{2}$

Sol :

Multiple Choice Questions (MCQs)

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Question 18

A rectangular parking lot has an area of $5 x^{2}+17 x+6$ square units. One of its sides is

(a) $(5 x+6)$

(b) $(x+2)$

(c) $(5 x+2)$

(d) $(5 x+1)$

Sol :

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Question 19

The complete factorisation of $-12 b^{5}-b^{3}+b$ is

(a) $-b\left(12 b^{4}+b^{2}-1\right)$

(b) $b(2 b-1)(2 b+1)\left(1+3 b^{2}\right)$

(c) $-b\left(4 b^{2}-1\right)\left(3 b^{2}+1\right)$

(d) $b(1-2 b)(1+2 b)\left(1+3 b^{2}\right)$

Sol :

High Order Thinking Skills (HOTS)

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Question 20

The binomial $x-3$ is not a factor of which of the following trinomials ?

(a) $2 x^{2}-x-15$

(b) $3 x^{2}-13 x+12$

(c) $2 x^{2}-8 x+6$

(d) $2 x^{2}-7 x-3$

Sol :

S.chand Class 8 Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 F

Exercise 6 F

Factorise :

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Question 1

$a^{2}+5 a+6$

Sol :

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Question 2

$x^{2}+7 x+12$

Sol :

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Question 3

$m^{2}+13 m+42$

Sol :

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Question 4

$a^{2}+25 a-54$

Sol :

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Question 5

$t^{2}+9 t-36$

Sol :

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Question 6

$a^{2}+5 a-50$

Sol :

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Question 7

$x^{2}-4 x-5$

Sol :

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Question 8

$y^{2}-10 y+16$

Sol :

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Question 9

$x^{2}-2 x-24$

Sol :

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Question 10

$y^{2}+2 y-48$

Sol :

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Question 11

$n^{2}-3 n-40$

Sol :

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Question 12

$y^{2}-11 y+24$

Sol :

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Question 13

$48+22 x-x^{2}$

Sol :

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Question 14

$x^{2}-29 x+204$

Sol :

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Question 15

$p^{2}-5 p-176$

Sol :

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Question 16

$n^{2}-19 n-92$

Sol :

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Question 17

$j^{2}-11 j-102$

Sol :

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Question 18

$2 a^{3}+10 a^{2}-28 a$ [Hint. First take out the common factor $2 a$.]

Sol :

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Question 19

$12 b+15-3 b^{2}$

Sol :

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Question 20

$3 c^{5}-18 c^{4}-48 c^{3}$

Sol :

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Question 21

$b^{2} c^{3}+8 b c^{4}+12 c^{5}$

Sol :

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Question 22

$a^{4}-5 a^{2}-36$

Sol :

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Question 23

$y^{4}+4 y^{2}-32$

Sol :

Multiple Choice Questions (MCQs)

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Question 24

Which is the correct factorisation of $x^{2}-10 x-24$ ?

(a) $(x-2)(x+12)$

(b) $(x+4)(x-6)$

(c) $(x-4)(x-6)$

(d) $(x+2)(x-12)$

Sol :

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Question 25

One of the factors of $(x-y)^{2}-4(x-y)-45$ is

(a) $(x-y+9)$

(b) $(x-y-5)$

(c) (x-y-9)

(d) (x+y+5)

High Order Thinking Skills (HOTS)

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Question 26

Which value of $b$ would make $y^{2}+b y-24$ factorable ?

(a) 14

(b) 11

(c) 5

(d) 25

Sol :

S.chand Class 8 Composite Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 E

Exercise 6 E

Factorise the following expressions :

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Question 1

$a^{2}-4$

Sol :

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Question 2

$25-x^{2}$

Sol :

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Question 3

$9 b^{2}-16$

Sol :

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Question 4

$49 p^{2}-16$

Sol :

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Question 5

$a^{2}-b^{2}$

Sol :

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Question 6

$a^{2} x^{2}-y^{2}$

Sol :

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Question 7

$49 c^{2}-25 d^{2}$

Sol :

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Question 8

$100-r^{2}$

Sol :

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Question 9

$49 a^{2}-1$

Sol :

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Question 10

$100 b^{2}-81$

Sol :

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Question 11

$x^{2} y^{2}-4$

Sol :

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Question 12

$1-d^{2}$

Sol :

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Question 13

$b^{4}-100$

Sol :

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Question 14

$25-a^{2} x^{2} $

Sol :

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Question 15

$144-a^{6}$

Sol :

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Question 16

$b^{4}-a^{2}$

Sol :

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Question 17

$a^{2} b^{2}-y^{2}$

Sol :

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Question 18

$\frac{1}{4} b^{2}-49$

Sol :

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Question 19

$c^{2}-0.36$

Sol :

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Question 20

$x^{2}-\frac{1}{9}$

Sol :

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Question 21

$\frac{4}{25} m^{2}-64$

Sol :

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Question 22

$\frac{x^{2}}{9}-\frac{y^{2}}{4}$

Sol :

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Question 23

$\frac{36}{a^{2}}-\frac{25}{b^{2}}$

Sol :

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Question 24

$x^{2}-0.01$

Sol :

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Question 25

$81-(x-7)^{2}$

Sol :

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Question 26

$x^{3}-x$

Sol :

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Question 27

$18 a^{2} x^{2}-32$

Sol :

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Question 28

$3 x^{3} y-243 x y^{3}$

Sol :

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Question 29

$a^{4}-81$

Sol :

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Question 30

$x^{4}-y^{4}$

Sol :

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Question 31

$a^{4}-16 x^{4} \quad$ 32. $x^{2}-y^{2}+2 x+1$

Sol :

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Question 32

$x^{2}+4 y^{2}-z^{2}-4 x y$

Sol :

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Question 33

$x^2+4y^2-z^2-4xy$

Sol :

Multiple Choice Questions (MCQs)

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Question 34

$25(x+y)^{2}-36(x-2 y)^{2}$ can be factorised as :

(a) $(5 x-12 y)(-6 x+5 y)$

(b) $(11 x-7 y)(-x+17 y)$

(c) $(-11 x+7 y)(x-17 y)$

(d) $(-5 x+12 y)(6 x-5 y)$

Sol :

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Question 35

One of the factors of $x^{2}+y^{2}+2 x y-z^{2}$ is

(a) $(x-y+z)$

(b) $(x+y-z)$

(c) $(-x-y+z)$

(d) $(-x+y-z)$

Sol :

High Order Thinking Skills (HOTS)

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Question 36

Factorize $\left(256 x^{16}-1\right)$

Sol :

S.chand Class 8 Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 D

Exercise 6 D

A. Which are perfect trinomial squares ? Write Yes or No.

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Question 1

$a^{2}+10 a+16$

Sol :

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Question 2

$b^{2}+14 b-49$

Sol :

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Question 3

$x^{2}-5 x+4$

Sol :

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Question 4

$x^{2}+10 x+25$

Sol :

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Question 5

$c^{2}-2 c d-d^{2}$

Sol :

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Question 6

$81 a^{2}-72 a b+16 b^{2}$

Sol :

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Question 7

$36 d^{2}+13 d x+x^{2}$

Sol :

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Question 8

$4 x^{2}+4 x+1$

Sol :

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Question 9

$49 m^{2}+140 m n+100 n^{2}$

Sol :

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Question 10

$16 b^{2}-20 b y+25 y^{2}$

Sol :

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Question 11

$25 x^{4}-60 x^{2} y^{2}+36 y^{4}$

Sol :

B. Fill in the missing term, making a perfect trinomial square :

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Question 12

$n^{2}+?+49$

Sol :

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Question 13

$x^{2}-?+25$

Sol :

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Question 14

$b^{2}-?+9$

Sol :

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Question 15

? + $16 x+64$

Sol :

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Question 16

$p^{2}-10 p q+$ ?

Sol :

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Question 17

$?-12 x+9$

Sol :

C. Factorise the following trinomials :

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Question 18

$a^{2}+2 a+1$

Sol :

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Question 19

$b^{2}+4 b+4$

Sol :

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Question 20

$y^{2}-8 y+16$

Sol :

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Question 21

$36-12 r+r^{2}$

Sol :

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Question 22

$81+18 x+x^{2}$

Sol :

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Question 23

$9 d^{2}-6 d+1$

Sol :

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Question 24

$1-8 a x+16 a^{2} x^{2}$

Sol :

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Question 25

$16 a^{2}-40 a b+25 b^{2}$

Sol :

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Question 26

$x^{2}+5 x+\frac{25}{4}$

Sol :

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Question 27

$49 x^{4}-168 x^{2} y^{2}+144 y^{4}$

Sol :

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Question 28

$a^{2}+a+\frac{1}{4}$

Sol :

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Question 29

$\frac{x^{2}}{4 y^{2}}-\frac{2}{3}+\frac{4 y^{2}}{9 x^{2}}$

Sol :

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Question 30

$\frac{x^{2}}{4 y^{2}}-\frac{1}{3}+\frac{y^{2}}{9 x^{2}}$

Sol :

D. Find the square root of the following trinomials :

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Question 31

$64-16 y+y^{2}$

Sol :

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Question 32

$144+24 x+x^{2}$

Sol :

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Question 33

$49 y^{2}-56 y+16$

Sol :

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Question 34

$64-176 x+121 x^{2}$

Sol :

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Question 35

$\frac{a^{2}}{b^{2}}+2+\frac{b^{2}}{a^{2}}$.

Sol :

Multiple Choice Questions (MCQs)

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Question 36

Factorization of the polynomial $(x-y)^{2} a^{2}+2(x-y)(x+y) a b+(x+y)^{2} b^{2}$ gives

(a) $(a x-b y)(a x+b y)$

(b) $(a x+b y)(b x+a y)$

(c) $(a x-a y+b x+b y)^{2}$

(d) $(a x+a y+b x+b y)^{2}$

Sol :

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Question 37

The area of a square is $4 x^{2}+20 x+25$. Which expression represents a side of the square ?

(a) $(2 x-5)$

(b) $(5-2 x)$

(c) $(2 x+5)$

(d) $\left.2 x^{2}+5\right)$

Sol :

High Order Thinking Skills (HOTS)

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Question 38

For what value of $c$ are the factors of $\left(x^{2}-c x+\frac{81}{16}\right)$ the same?

Sol :

S.chand Class 8 Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 C

Exercise 6 C

Factorise :

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Question 1

$a x^{2}+b y^{2}+b x^{2}+a y^{2}$

Sol :

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Question 2

$a^{2}+2 b+a b+2 a$

Sol :

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Question 3

px+qx+py+qy

Sol :

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Question 4

$x^{3}+3 x^{2}+6 x+18$

Sol :

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Question 5

$x^{2}-a x-b x+a b$
Sol :

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Question 6

3ac+2bc+3ad+2bd

Sol :

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Question 7

8pr+4qr+6ps+3qs

Sol :

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Question 8

7ab+9cd+7ad+9bc

Sol :

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Question 9

3mn+2pn+3mq+2pq

Sol :

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Question 10

10pq-3rq-10ps+3rs

Sol :

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Question 11

$a b^{2}-b c^{2}-a b+c^{2}$

Sol :

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Question 12

$2 b^{2}+8 a b+4 a c+b c$

Sol :

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Question 13

6pm+9mq+8pn+12qn

Sol :

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Question 14

$2 a x y^{2}+10 x+3 a y^{2}+15$

Sol :

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Question 15

$a x y^{2}+3 x+2 a^{2} y^{2}+6 a$

Sol :

Multiple Choice Questions (MCQs)

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Question 16

$x y\left(z^{2}+1\right)+z\left(x^{2}+y^{2}\right)$ can be factorised as

(a) $(x y+z)(y z+x)$

(b) $(z x+y)(x y+z)$

(c) $(y z+x)(z x+y)$

(d) $\left(x^{2}+y^{2}\right)(z+x)$

Sol :

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Question 17

The polynomial $a^{2}-b+a b-a$ on factorization reduces to

(a) $(a+b)\left(a^{2}+b^{2}\right)$

(b) $(a+b)(a+1)$

(c) $(a-b)(a+b)$

(d) $(a+b)(a-1)$

Sol :

S.chand Class 8 Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 B

Exercise 6 B

Factorise the following polynomials :

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Question 1

z(z-1)+2(z-1)

Sol :

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Question 2

6(3+x)+x(3+x)

Sol :

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Question 3

2y(y+5)-3(y+5)

Sol :

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Question 4

5t(t-4)-6(t-4)

Sol :

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Question 5

5(2+b)-6b(2+b)

Sol :

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Question 6

x(x+11)+(x+11)

Sol :

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Question 7

p(6-p)-(6-p)

Sol :

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Question 8

d(d-5)+7(5-d)

Sol :

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Question 9

$(x+2)^{2}+5(x+2)$

Sol :

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Question 10

$(y-2)^{2}-3(y-2)$

Sol :

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Question 11

$14(3 y-5 z)^{3}+7(3 y-5 z)^{2}$

Sol :

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Question 12

$(n-10)^{2}+(10-n)$

Sol :

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Question 13

$5 x+10 y-7(x+2 y)^{2}$

Sol :

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Question 14

$(x+y)(3 x-7)-(x+y)(2 x-11)$

Sol :

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Question 15

$(3 a-1)^{2}-6 a+2$

Sol :

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Question 16

x(x-2z)+y(x-2z)+(2z-x)

Sol :

S.chand Class 8 Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 A

Exercise 6 A

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Factorise the following polynomials :

Question 1

3x-12

Sol :

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Question 2

80+16y

Sol :

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Question 3

8x-8y

Sol :

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Question 4

7x+14

Sol :

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Question 5

$a^{2}+7 a$

Sol :

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Question 6

$5 y-7 y^{2}$

Sol :

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Question 7

$8 c^{2}-24 c$

Sol :

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Question 8

$5 m^{2}-6 m$

Sol :

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Question 9

12u-20uv

Sol :

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Question 10

$10 p q-12 p^{2} q$

Sol :

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Question 11

$24 d+32 d^{3}$

Sol :

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Question 12

30g+54gh

Sol :

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Question 13

$28 c^{2} d^{2}-21 c^{2} d$

Sol :

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Question 14

$36 y^{3} z+48 y^{2} z^{2}$

Sol :

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Question 15

$6 p+8 p^{2}-4 p^{3}$

Sol :

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Question 16

$12 a^{3}-15 a^{2}-7 a$

Sol :

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Question 17

$15 y^{2} z^{3}-20 y^{3} z^{4}+35 y^{2} z^{2}$

Sol :

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Question 18

$14 m^{5} n^{4} p^{2}-42 m^{7} n^{3} p^{7}-70 m^{6} n^{4} p^{3}$

Sol :

S.chand publication New Learning Composite mathematics solution of class 8 Chapter 6 Factorisation of Algebraic Expressions Exercise 6G

Exercise 6G

Q1 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Factorise:

Question 1

2x² + 11x + 15

Sol :

=2x²+6x+5x+15

=2x(x+3)+5(x+3)

=(2x+5)(x+3)

Q2 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 2

6x² + 17x + 5

Sol :

=6x²+15x+2x+5

=3x(2x+5)+1(2x+5)

=(3x+1)(2x+5)

Q3 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 3

3x² + 11x + 10

Sol :
=3x²+6x+5x+10

=3x(x+2)+5(x+2)

=(3x+5)(x+2)

Q4 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 4

5b² + 16b + 3

Sol :
=5b²+15b+b+3

=5b(b+3)+1(b+3)

=(b+3)(5b+1)

Q5 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 5

3x² + 13x + 12

Sol :

=3x²+9x+4x+12

=3x(x+3)+4(x+3)

=(x+3)(3x+4)

Q6 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 6

2x² + 17x + 21

Sol :

=2x²+14x+3x+21

=2x(x+7)+3(x+7)

=(2x+3)(x+7)

Q7 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 7

15y² + 16y + 4

Sol :

=15y²+10y+6y+4

=5y(3y+2)+2(3y+2)

=(3y+2)(5y+2)

Q8 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 8

6x² – 17x -14

Sol :

=6x²–21x-4x-14

=3x(2x+7)-2(2x+7)

=(2x+7)(3x-2)

Q9 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 9

4m² + 7m – 2

Sol :

=4m²+8m-m-2

=4m(m+2)-1(m+2)

=(m+2)(4m-1)

Q10 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 10

2x² – 7x – 15

Sol :

=2x²–10x+3x-15

=2x(x-5)+3(x-5)

=(x-5)(2x+3)

Q11 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 11

5x² – 16x + 3

Sol :

=5x²–15x-x+3

=5x(x-3)-1(x-3)

=(x-3)(5x-1)

Q12 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 12

6x² – 17x + 12

Sol :

=6x²-9x-8x+12

=3x(2x-3)-4(2x-3)

=(2x-3)(3x-4)

Q13 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 13

5x² + 9x – 18

Sol :

=5x²+15x-6x-18

=5x(x+3)-6(x+3)

=(x+3)(5x-6)

Q14 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 14

3x² – x – 4

Sol :
=3x²–4x+3x-4

=x(3x-4)+1(3x-4)

=(3x-4)(x+1)

Q15 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 15

8a² + 18a – 5

Sol :

=8a²+20a-2a-5

=4a(2a+5)-1(2a+5)

=(2a+5)(4a-1)

Q16 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 16

8x² – 73x + 9

Sol :

=8x²–72x-x+9

=8x(x-9)-1(x-9)

=(x-9)(8x-1)

Q17 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 17

-2x² + 5x + 42

Sol :

=-2x²+12x-7x+42

=-2x(x-6)-7(x-6)

=(x-6)(-2x-7)

Q18 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 18

-12x² – 35x – 18

Sol :
=-12x²–27x-8x-18

=-3x(4x+9)-2(4x+9)

=(4x+9)(-3x-2)

Q19 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 19

-2x² – 15x – 7

Sol :
=-2x²–14x-x-7

=-2x(x+7)-1(x+7)

=(x+7)(-2x-1)

Q20 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 20

30t² + 39t – 9

Sol :

=30t²+45t-6t-9

=15t(2t+3)-3(2t+3)

=(2t+3)(15t-3)

Q21 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 21

15x⁴ – 10x³ – 25x²

Sol :

=5x²(3x²-5x+3x-5)

=5x²[x(3x-5)+1(3x-5)]

=5x²[(3x-5)(x+1)]

Q22 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 22

14x³ – 57x²y – 27xy²

Sol :

=14x³–63x²y+6x²y-27xy²

=7x²(2x-9y)+3xy(2x-9y)

=(2x-9y)(7x²+3xy)

=x(7x+3y)(2x-9y)

Q23 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 23

-3x³ + 16x² – 16x

Sol :

=x(-3x²+16x–16)

=x[-3x²+16x-16]

=x[-3x²+12x+4x-16]

=x[-3x(x-4)+4(x-4)]

=x[(x-4)(-3x+4)]

Q24 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 24

-4x⁴ – 4x³ + 15x²

Sol :

=x²(-4x²-4x+15)

=x²(-4x²-10x+6x+15)

=x²[-2x(2x-5)+3(x-5)]

=x²[(2x-5)(-2x+3)]

Q25 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 25

56x³ + 15x² – 56x

Sol :

=x(56x²+15x-56)

=x[56x²-49x+64x-56]

=x[7x(8x-7)+8(8x-7)]

=x(8x-7)(7x+8)

Q26 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 26

32x⁴ + 12x³y – 5x²y²

Sol :
=32x⁴+20x³y-8x³y-5x²y²

=4x³(8x+5y)-x²y(8x+5y)

=(8x+5y)(4x³-x²y)

=x²(4x-y)(8x+5y)

Q27 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 27

30m² – 78mn + 36n²

Sol :

=30m²–60mn-18mn+36n²

=30m(m-n)-18n(m-n)

=(m-2n)(30m-18n)

=6(5m-3n)(m-2n)