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S.chand Class 8 Maths Solution Chapter 5 Algebraic Expressions and Special Products Exercise 5 G

Exercise 5 G

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Question 1

Find the following products :

(i) (x+2)(x-2)

Sol :

(ii) $(d-8)(d+8)$

Sol :

(iii) $(5+9 m)(5-9 m)$

Sol :

(iv) $\left(x^{2}-y^{2}\right)\left(x^{2}+y^{2}\right)$

Sol :

(v) $\left(\frac{2}{5} a b-c\right)\left(\frac{2}{5} a b+c\right)$

Sol :

(vi) $\left(\frac{2}{b}-\frac{5}{c}\right)\left(\frac{2}{b}+\frac{5}{c}\right)$

Sol :

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Question 2

(i) $(a+1)(a-1)\left(a^{2}+1\right)$

Sol :

(ii) $(a+x)(a-x)\left(a^{2}+x^{2}\right)$

Sol :

(iii) $\left(x-\frac{1}{x}\right)\left(x+\frac{1}{x}\right)\left(x^{2}+\frac{1}{x^{2}}\right)$

Sol :

(iv) $\left(x^{3}-\frac{1}{x^{3}}\right)\left(x^{3}+\frac{1}{x^{3}}\right)\left(x^{6}+\frac{1}{x^{6}}\right)$.

Sol :

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Question 3

Using the identity for difference of two squares, find the values of :

(i) $18 \times 22$

(ii) $101 \times 99$

(iii) $(84)^{2}-(76)^{2}$

(iv) $(203)^{2}-(197)^{2}$

Sol :

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Question 4

Find the value of $x$, if :

(i) $13 x=(58)^{2}-(45)^{2}$

(ii) $24 x=(99)^{2}-(87)^{2}$

Sol :

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Question 5

Simplify :

(i) $179 \times 179-21 \times 21$

(ii) $1.62 \times 1.62-0.38 \times 0.38$

(iii) $\frac{297 \times 297-203 \times 203}{94}$ [Hint. $\left.94=297-203\right]$

(iv) $\frac{23.71 \times 23.71-16.29 \times 16.29}{0.742}$.

Sol :

Multiple Choice Questions (MCQs)

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Question 6

$(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right)\left(1+x^{8}\right)(1-x)$

(a) $1+x^{16}$

(b) $1-x^{16}$

(c) $x^{16}-1$

(d) $x^{8}+1$

Sol :

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Question 7

$\frac{4.359 \times 4.359-1.641 \times 1.641}{4.359-1.641}=$ ?

(a) $6.3$

(b) 6

(c) $3.2$

(d) $4.6$

Sol :

High Order Thinking Skills (HOTS)

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Question 8

$\frac{3.7 \times 3.7+2.3 \times 2.3+2 \times 3.7 \times 2.3}{4.6 \times 4.6-3.4 \times 3.4}$ equals

(a) $3 \frac{3}{4}$

(b) $4 \frac{3}{4}$

(c) $3 \frac{1}{4}$

(d) $3 \frac{1}{2}$

Sol :

S.chand Class 8 Maths Solution Chapter 5 Algebraic Expressions and Special Products Exercise 5 F

Exercise 5 F

Q1 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 1

Write down the squares of :

(i) p+5

Sol :

(ii) 2t+9

Sol :

(iii) 5c+2d

Sol :

(iv) $9 m+\frac{1}{4}$

Sol :

(v) $3 x+\frac{1}{3 x}$

Sol :

(vi) $\left(2 y^{2}+5 z^{2}\right)$

Sol :

(vii) $\left(7 x^{3}+\frac{1}{7} y^{3}\right)$

Sol :

(viii) $\left(\frac{1}{2} a^{4}+\frac{1}{3} b^{7}\right)$

Sol :

(ix) t-3

Sol :

(x) 7p-8q

Sol :

(xi) $8 m-\frac{1}{2}$

Sol :

(xii) $3 m^{3}-7 n^{4}$

Sol :

(xiii) $x^{3}-\frac{1}{x^{3}}$

Sol :

(xiv) $\frac{1}{5} p^{5}-\frac{1}{2} q^{6}$

Sol :

Q2 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 2

Simplify:

(i) $\left(a^{3} b-x y^{3}\right)^{2}$

Sol :

(ii) $\left(\frac{3}{5} a-10 b\right)^{2}$

Sol :

(iii) $\left(2 x^{2}+\frac{1}{3 x^{2}}\right)^{2}$

Sol :

(iv) $\left(5 m^{3}-\frac{1}{5 m^{3}}\right)^{2}$

Sol :

Q3 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 3

Using the identity for square of a binomial, evaluate the following:

(i) $(102)^{2}$

Sol :

(ii) $(501)^{2}$

Sol :

(iii) $(709)^{2}$

Sol :

(iv) $(59)^{2}$

Sol :

(v) $(199)^{2}$

Sol :

(vi) $(999)^{2}$

Sol :

Q4 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 4

Find the value of the expression : $25 x^{2}+70 x+49$ if $x=-1$

Sol :

Q5 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 5

If $\left(x+\frac{1}{x}\right)=12$, find the value of $\left(x^{2}+\frac{1}{x^{2}}\right)$

Sol :

Q6 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 6

If $\left(x+\frac{1}{x}\right)=5$, find the values of $\left(x^{2}+\frac{1}{x^{2}}\right)$ and $\left(x^{4}+\frac{1}{x^{4}}\right)$.

Sol :

Q7 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 7

If $x-\frac{1}{x}=7$, find the value of $\left(x^{2}+\frac{1}{x^{2}}\right)$

Sol :

Q8 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 8

If $x-\frac{1}{x}=8$, find the values of $\left(x^{2}+\frac{1}{x^{2}}\right)$ and $\left(x^{4}+\frac{1}{x^{4}}\right)$.

Sol :

Q9 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 9

If $x+y=9$ and $x y=16$, find the value of $\left(x^{2}+y^{2}\right)$.

Sol :

Multiple Choice Questions (MCQs)

Q10 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 10

$(t-3)^{2}-(t+3)^{2}$ equals

(a) $2 t^{2}+18$

(b) $-12 t$

(c) $12 t$

(d) 18

Sol :

Q11 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 11

If $x^{2}+\frac{1}{x^{2}}=27$, find the value of $x-\frac{1}{x}$

(a) 5

(b) 29

(c) $\sqrt{29}$

(d) 57

Sol :

Q12 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 12

If $x-y=9$ and $x y=16$, find the value of $x^{2}+y^{2}$

(a) 113

(b) 49

(c) 65

(d) 97

Sol :

High Order Thinking Skills (HOTS)

Q13 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 13

If $\left(a x^{3}+2\right)^{2}=a^{2} x^{6}+x^{3}+4$, then find $a$.

Sol :

Q14 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 14

If $\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{10}{3}$ and x+y=10 ,then find $x y$.

Sol :

S.chand Class 8 Maths Solution Chapter 5 Algebraic Expressions and Special Products Exercise 5 E

Exercise 5 E

Divide :

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Question 1

$a^{2}+6 a+5$ by $a+1$

Sol :

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Question 2

$x^{2}-3 x+2$ by $x-1$

Sol :

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Question 3

$x^{2}+4 x-21$ by $x+7$

Sol :

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Question 4

$14-17 x+5 x^{2}$ by $2-x$

Sol :

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Question 5

$14 x^{2}+13 x-15$ by $7 x-4$

Sol :

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Question 6

$x^{3}+3-4 x+2 x^{2}$ by $x-2$

Sol :

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Question 7

$x^{4}+4 x-2 x^{2}+x^{3}-10$ by $x-2$

Sol :

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Question 8

$8 x^{2}+21 x+x^{3}+18$ by $6+5 x+x^{2}$

Sol :

Using division find whether or not the first polynomial is a factor of the second:

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Question 9

$x-7 ; x^{2}-3 x-28$

Sol :

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Question 10

$2 x-3 ; 6 x^{3}+x^{2}-19 x+6$

Sol :

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Question 11

$x-6 ; x^{2}-12 x+40$

Sol :

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Question 12

$6 p^{3}+5 p^{2}+4$ by $(2 p+1)$

Sol :

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Question 13

$x^{3}+4 x-3$ by $(x+5)$

Sol :

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Question 14

What should be added to $6 x^{5}+4 x^{4}-27 x^{3}-7 x^{2}-27 x-6$ so that the resulting polynomial is exactly divisible by $\left(2 x^{2}-3\right)$.

Sol :

Multiple Choice Questions (MCQs)

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Question 15

What will be the remainder when $6 x^{5}+4 x^{4}-27 x^{3}$ $-7 x^{2}+27 x+\frac{3}{2}$ is divided by $\left(2 x^{2}-3\right) ?$

(a) $\frac{1}{2}$

(b) $-\frac{1}{2}$

(c) 0

(d) $-\frac{9}{2}$

Sol :

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Question 16

What should be subtracted from $8 x^{4}+14 x^{3}$ $-2 x^{2}+7 x-8$ so that the resulting polynomial is exactly divisible by $4 x^{2}+3 x-2$.

(a) $-14 x+10$

(b) $13 x-9$

(c) $14 x-10$

(d) $-10$

Sol :

S.chand Class 8 Maths Solution Chapter 5 Algebraic Expressions and Special Products Exercise 5 D

Exercise 5 D

Q1 | Ex-5D | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 1

Divide

(i) $x^{5} \div x^{3}$

(ii) $y^{7} \div y^{3}$

(iii) $a^{9} \div a^{4}$

(iv) $x^{3} \div x$

(v) $a^{3} b^{4} \div a^{2} b$

(vi) $a^{3} b^{7} \div a^{4} b^{6}$

(vii) $-54 x^{4} y^{5} \div 6 x^{2} y^{3}$

(viii) $84 a^{2} b^{5} \div 12 a^{2} b^{2}$

Q2 | Ex-5D | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 2

Divide :

(i) $8 x+4$ by 2

(ii) $6 y-3$ by 3

(iii) $12 y^{2}+36$ by $-4$

(iv) $-40 x-30$ by $-10$

(v) $3 b-3$ by $-3$

(vi) $x^{3}-x^{2}$ by $x$

(vii) $5 c^{2}-c$ by $-c$

(viii) $10 a^{3}+12 a b$ by $2 a$

(ix) $9 x^{2} y^{2}+3 x^{2} y-6 x y^{2}$ by $3 x y$

(x) $6 a^{2} b^{2}-3 a b c+9 a b d$ by $-\frac{1}{3} a b$

Q3 | Ex-5D | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 3

Multiple Choice Questions (MCQs)

If $-15 m n^{4} p^{2}$ is divided by $\frac{1}{6} m^{4} n^{4} p^{2}$. The quotient is

(a) $\frac{-5}{3 m^{3}}$

(b) $\frac{-90 n^{8} p^{4}}{m^{3}}$

(d) $-90 m^{3}$

Q4 | Ex-5D | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 4

$\frac{-7 x^{7} y^{3}}{x^{7}}-\frac{56 x y^{5} z^{2}}{-8 x y^{2} z^{2}}$ equals

(a) $-15 y^{3}$

(b) $15 y^{3}$

(d) $y^{3}$

High Order Thinking Skills (HOTS)

Q5 | Ex-5D | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 5

In which of the following division problems, the quotient is not a polynomial.

(a) $x^{4} y-2 x^{3} y^{2}+x^{5} y^{5}$ by $x^{2} y$

(b) $-10 x^{3} y^{2}+15 x^{2} y^{3}-5 x^{2} y^{2}$ by $\frac{-5}{2} x^{2} y^{2}$

(c) $4 x^{2} y-7 x y^{2}-y^{2}$ by $-x^{2} y^{2}$

S.chand Class 8 Maths Solution Chapter 5 Algebraic Expressions and Special Products Exercise 5 C

Exercise 5 C

Q1 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 1

Multiply :

(x+2)(x+5)

Sol :

Q2 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 2

(x-4)(x+9)

Sol :

Q3 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 3

(x-7)(x-9)

Sol :

Q4 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 4

$(x^2+5)(x^2-6)$

Sol :

Q5 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 5

$(5 x-3 y)(3 x+4 y)$

Sol :

Q6 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 6

$\left(5 x^{2}+2 y^{2}\right)\left(3 x^{2}-7 y^{2}\right)$

Sol :

Q7 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 7

$\left(3 x+\frac{5 y}{7}\right)\left(2 x-\frac{3 y}{7}\right)$

Sol :

Q8 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 8

$\left(\frac{1}{7} x-\frac{1}{8} y\right)\left(7 x^{2}-8 y^{2}\right)$

Sol :

Q9 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 9

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

Sol :

Q10 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 10

Multiply $\left(4 x^{2}+3 y\right)$ by $\left(3 x^{2}-4 y\right)$ and verify the result for $x=1, y=2$

Sol :

Q11 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 11

Simplify :

(i) $\frac{2}{7}\left(14 x^{2}-21 y^{2}\right)\left(-5 x^{2}-3 y^{2}\right)$

(ii) $(2 x-3)(5 x+2)+(3 x-7)(4 x-1)$

Sol :

Q12 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 12

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

Sol :

Q13 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 13

$(3 x-7)\left(5 x^{2}-2 x+3\right)$

Sol :

Q14 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 14

$\left(x^{2}-2\right)\left(9 x^{2}-2 x+5\right)$

Sol :

Q15 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 15

$(x-3)\left(x^{3}+3 x^{2}-7 x+1\right)$

Sol :

Q16 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 16

$(x+y-3)(4 x-7 y+2)$

Sol :

Q17 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 17

$\left(x^{2}-7 x+2\right)\left(x^{2}+5 x-4\right)$

Sol :

Q18 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 18

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

Sol :

Q19 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 19

Simplify :

$(3 x-4)\left(2 x^{2}-5 x+1\right)-(2 x-1)\left(3 x^{2}+7 x-5\right)$

Multiple Choice Questions (MCQs)

Q20 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 20

Which of the following products is equal to $x^{2}-5 x-6 ?$

(a) (x+1)(x-6)

(b) (x-2)(x-3)

(c) (x+2)(x-3)

(d) (x-1)(x-5)

Sol :

Q21 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 21

$(x-y)\left(x^{2}+x y+y^{2}\right)$ equals

(a) $x^{3}-2 x^{2} y+2 x y^{2}-y^{3}$

(b) $x^{3}+y^{3}$

(c) $x^{3}-y^{3}$

(d) $x^{3}+2 x^{2} y-2 x y^{2}+y^{3}$

Sol :

High Order Thinking Skills (HOTS)

Q22 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 22

If (x+4)(x+1)-(x-1)(x-2)=0, what is the value of x ?

Sol :

Q23 | Ex-5C | Class 8 | SChand | Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 23

'Write a polynomial that represents the product of three consecutive odd integers, the first one being $(2 x-1)$.

Sol :

S.chand Class 8 Maths Solution Chapter 5 Algebraic Expressions and Special Products Exercise 5 B

Exercise 5 B

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Find the products

Question 1

(i) $-3 x^{2} y$ by $-5 x y^{2}$

(ii) $\frac{-3}{8} x^{4} y z$ by $-16 a^{2} y^{4} b^{3}$

(iii) $\left(\frac{-17}{8} x^{3} y^{2}\right) \times\left(\frac{-16}{51} x^{2} y\right)$

Sol :

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Question 2

$(-2 x y)\left(-3 x^{3} y^{2}\right)\left(-\frac{1}{6} x^{2} y^{7}\right)$

Sol :

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Question 3

$\left(\frac{5}{2} x^{2} y^{3}\right) \times\left(-y^{2} z\right) \times\left(-2 x^{3} y z^{7}\right) \times\left(\frac{-1}{5} x y z\right)$

Sol :

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Question 4

Find the value : (i) $\left(-10 m^{2} n^{6}\right) \times\left(-20 m n^{15}\right)$ for m=1.2 and n=-1.

Sol :

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Question 5

-4(5 y+7)

Sol :

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Question 6

-6(-m-3)

Sol :

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Question 7

$-2\left(2 x^{2}+3 x y-4 y^{2}\right)$

Sol :

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Question 8

$2 y\left(-y^{2}+3 y-4\right)$

Sol :

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Question 9

$x^{2} y\left(3 x^{2} y^{2}-5 x y+7\right)$

Sol :

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Question 10

$-2 c^{2}\left(4 c^{3}-10 c^{2}-8 c+9\right)$

Sol :

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Question 11

$-x^{2} y^{2}\left(x^{4}+x^{2} y^{2}-y^{4}\right)$

Sol :

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Question 12

100 x(0.01 x-0.19 y z)

Sol :

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Simplify :

Question 13

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

Sol :

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Question 14

$x^{2}\left(3-5 y^{2}\right)+x\left(x y^{2}-3 x\right)-2 y\left(y-2 x^{2} y\right)$.

Sol :

Multiple Choice Questions (MCQs)

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Question 15

The degree of $\left(-\frac{1}{20} x^{4} y^{3}\right) \times\left(-5 x^{7} y^{2}\right)$ is

(a) 11

(b) 5

(c) 16

(d) 6

Sol :

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Question 16

Simplify :

$x y^{2}(-2 x)(3 x y)\left(-4 x^{2} y\right)$ -$\left(\frac{1}{8} x^{2}\right)(-24 x y)\left(-\frac{4}{5} x^{2}\right)\left(15 y^{3}\right)$

(a) 1

(b) $x^{10} y^{8}$

(c) $-12 x^{5} y^{4}$

(d) $-12 x^{10} y^{8}$

Sol :

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Question 17

$42 a^{2}-8 a(a-1)-7 a(1+5 a)+a(a-1)$ equals

(a) $15 a^{2}$

(b) -16a

(c) 0

(d) $15 a^{2}-16 a$

Sol :

S.chand Class 8 Maths Solution Chapter 5 Algebraic Expressions and Special Products Exercise 5 A

Exercise 5 A

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Question 1

Add

(i) $5 x y,-2 x y,-11 x y, 8 x y$

(ii) $3 a^{2} b,-5 a^{2} b, 10 a^{2} b,-7 a^{2} b$

(iii) $a+b, 3 a+2 b$

(iv) $3 a-2 b+c, 5 a+8 b-7 c$

(v) $4 x^{2}-5 x y+3 y^{2}, 8 x^{2}+7 x y-6 y^{2},-2 x^{2}-9 x y+13 y^{2}$

Sol :

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Question 2

Subtract :

(i) $3 x-5$ from $8 x-17$

(ii) $-8 x y$ from $7 x y$

(iii) $2 x^{2}-5 x+10$ from $5 x^{2}-11 x+19$

(iv) $3 y^{2}-8 y+7$ from $9 y^{2}+5 y+6$

(v) $-7 p+2 q-3 r+5$ from $2 p-3 q-7 r-11$.

(vi) $5 m^{3}-3 m^{2}+7 m-8$ from $8 m^{3}-9 m^{2}+5 m-2$.

Sol :

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Question 3

Two adjacent sides of a rectangle are $3 x^{2}-5 y^{2}$ and $7 x^{2}-x y$. Find its perimeter.

Sol :

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Question 4

The perimeter of a triangle is $7 p^{2}-8 p+9$ and two of its sides are $2 p^{2}-p+1$ and $11 p^{2}-3 p+5$. Find the third side of the triangle.

Sol :

Multiple Choice Questions (MCQs)

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Question 5

$2 x^{4}-4 x^{2} y^{2}+5 y^{5}$ is a of degree

(a) Binomial; 4

(b) Trinomial; 2

(c) Trinomial; 5

(d) Monomial; 5

Sol :

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Question 6

Which of the following is not equal to $-6 t^{2}-t$ ?

(a) $-\left(6 t^{2}+t\right)$

(b) $\left(t^{2}+8 t\right)-\left(7 t^{2}+9 t\right)$

(c) $\left(3 t^{2}-5 t\right)-\left(-5 t^{2}-4 t\right)$

(d) $\left(2 t^{2}-3 t+1\right)-\left(8 t^{2}-2 t+1\right)$

Sol :