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

 Exercise 6E

Q1 | Ex-6E | Ch-6 | Cl-8 | Factorisation of Algebraic Expressions | New Learning Composite Maths | Schand | myhelper

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Question 1

(a)  y² – 9

Sol :

=y²-3² 

=(y+3)(y-3)

(b) x² – 25

Sol :

=x²-5²

=(x+5)(x-5)

(c) 9x² – 4

Sol :

=(3x)²-2²

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

(d) 49x² – 64

Sol :

=(7x)²-8²

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

(e) – 16 + x²

Sol :

=x²-16

=x²-4²

=(x+4)(x-4)

(f) p⁶ – 36

Sol :

=(p³)²-6²

=(p³+6)(p³-6)

(g) 144x⁴y² – z²

Sol :

=(12x²y)²-z²

=(12x²y+z)(12x²y-z)

(h) x⁶ – y⁴

Sol :

=(x³)²-(y²)² 

=(12x²y+z)(12x²y-z)

(i) $\frac{a^2}{9}-\frac{b^2}{16}$

Sol :

$=\left(\frac{a}{3}\right)^2-\left(\frac{b}{4}\right)^2$

$=\left(\frac{a}{3}+\frac{b}{4}\right) \left(\frac{a}{3}-\frac{b}{4}\right)$

(j) $\frac{121}{9}m^2-n^2$

Sol :

$=\left( \frac{11}{3}m \right)^2-n^2$

$=\left(\frac{11}{3}m+n\right)\left(\frac{11}{3}m-n\right)$

(k) $\frac{25}{36}x^8-y^4$

Sol :

$=\left(\frac{5}{6}x^4 \right)^2 -(y^2)^2$

$=\left(\frac{5}{6}x^4 +y^2 \right)\left(\frac{5}{6}x^4 -y^2 \right)$

(l) $-25+\frac{1}{64}b^2$

Sol :

$=\frac{1}{64}b^2-25$

$=\left(\frac{1}{8}b\right)^2+5^2$

$=\left(\frac{1}{8}b+5\right)\left(\frac{1}{8}b-5\right)$

Q2 | Ex-6E | Ch-6 | Cl-8 | Factorisation of Algebraic Expressions | New Learning Composite Maths | Schand | myhelper

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Question 2

(a) x² + 8x + 16 – y²

Sol :

=x²+2.4x+4²-y²

=(x+4)²-y²

=(x+4+y)(x+4-y)

(b) (a – b)² – x²

Sol :

=(a-b+x)(a-b-x)

(c) b² – 6b + 9 – c²

Sol :

=b²-2.3.b+3²-c²

=(b-3)²-c²

=(b-3+c)(b-3-c)

(d) y² – b² – 8b – 16

Sol :

=y²–(b²+8b+16)

=y²–(b²+2.b.4+4²)

=y²–(b+4)²

=(y+b+4)(y-b-4)

(e) x² – c² – 4 + 4c

Sol :

=x²–(c²+4-4c)

=x²–(c²-2.2c+4²)

=x²–(c-4²)

=(x+c-4)(x-c+4)

(f) a² – b² – 10bc – 25c²

Sol :

=a²–(b²+10bc+25c²)
=a²–(b²-2.b.5c+(5c)²)
=a²–(b+5c)²
=(a+b+5c)(a-b-5c)

Q3 | Ex-6E | Ch-6 | Cl-8 | Factorisation of Algebraic Expressions | New Learning Composite Maths | Schand | myhelper

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Question 3

(a) 5p² – 5

Sol :

=5(p²-1)=5(p²-1²)

=5[(p+1)(p-1)]

(b) 8a² – 32

Sol :

=8(a²–4)

=8(a²-2²)

=8(a+2)(a-2)

(c) 16 – 100x²y²

Sol :

=4²-(10xy)²

=(4+10xy)(4-10xy)

(d) 2a³b⁴ – 98ab²

Sol :

=2ab²(a²-49)

=2ab²(a²-7²)

=2ab²(a+7)(a-7)

(e) c² – 6c + 9 – y²

Sol :

=c²-2.3c+3²-y²

=(c-3)²-y²

=(c-3+y)(c-3-y)

(f) x³ + x² – 4x – 4

Sol :

=x³-4x+x²-4

=x(x²-4)+(x²-4)

={x(x²-2²)}+(x²-2²)

=[x(x+2)(x-2)+(x+2)(x+2)]

=(x+2)(x-2)[x+1]

(g) m³ – mn² – m² + n²

Sol :

=m³–m²–mn²+n²

=m²(m-1)-n²(m-1)

=(m²-n²)(m-1)

=(m-1)(m+1)(m-1)