Exercise 6 D
A. Which are perfect trinomial squares ? Write Yes or No.
Q1 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 1
$a^{2}+10 a+16$
Sol :
Q2 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 2
$b^{2}+14 b-49$
Sol :
Q3 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 3
$x^{2}-5 x+4$
Sol :
Q4 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 4
$x^{2}+10 x+25$
Sol :
Q5 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 5
$c^{2}-2 c d-d^{2}$
Sol :
Q6 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 6
$81 a^{2}-72 a b+16 b^{2}$
Sol :
Q7 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 7
$36 d^{2}+13 d x+x^{2}$
Sol :
Q8 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 8
$4 x^{2}+4 x+1$
Sol :
Q9 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 9
$49 m^{2}+140 m n+100 n^{2}$
Sol :
Q10 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 10
$16 b^{2}-20 b y+25 y^{2}$
Sol :
Q11 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
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 :
Q12 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 12
$n^{2}+?+49$
Sol :
Q13 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 13
$x^{2}-?+25$
Sol :
Q14 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 14
$b^{2}-?+9$
Sol :
Q15 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 15
? + $16 x+64$
Sol :
Q16 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 16
$p^{2}-10 p q+$ ?
Sol :
Q17 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 17
$?-12 x+9$
Sol :
C. Factorise the following trinomials :
Q18 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 18
$a^{2}+2 a+1$
Sol :
Q19 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 19
$b^{2}+4 b+4$
Sol :
Q20 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 20
$y^{2}-8 y+16$
Sol :
Q21 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 21
$36-12 r+r^{2}$
Sol :
Q22 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 22
$81+18 x+x^{2}$
Sol :
Q23 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 23
$9 d^{2}-6 d+1$
Sol :
Q24 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 24
$1-8 a x+16 a^{2} x^{2}$
Sol :
Q25 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 25
$16 a^{2}-40 a b+25 b^{2}$
Sol :
Q26 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 26
$x^{2}+5 x+\frac{25}{4}$
Sol :
Q27 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 27
$49 x^{4}-168 x^{2} y^{2}+144 y^{4}$
Sol :
Q28 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 28
$a^{2}+a+\frac{1}{4}$
Sol :
Q29 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 29
$\frac{x^{2}}{4 y^{2}}-\frac{2}{3}+\frac{4 y^{2}}{9 x^{2}}$
Sol :
Q30 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
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 :
Q31 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 31
$64-16 y+y^{2}$
Sol :
Q32 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 32
$144+24 x+x^{2}$
Sol :
Q33 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 33
$49 y^{2}-56 y+16$
Sol :
Q34 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 34
$64-176 x+121 x^{2}$
Sol :
Q35 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 35
$\frac{a^{2}}{b^{2}}+2+\frac{b^{2}}{a^{2}}$.
Sol :
Multiple Choice Questions (MCQs)
Q36 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
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 :
Q37 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
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)
Q38 | Ex-6D | Class 8 | SChand Composite Maths | Factorisation of Algebraic Expressions | myhelper
Question 38
For what value of $c$ are the factors of $\left(x^{2}-c x+\frac{81}{16}\right)$ the same?
Sol :
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