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


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) a29b216

Sol :

=(a3)2(b4)2

=(a3+b4)(a3b4)


(j) 1219m2n2
Sol :
=(113m)2n2

=(113m+n)(113mn)

(k) 2536x8y4

Sol :

=(56x4)2(y2)2

=(56x4+y2)(56x4y2)


(l) 25+164b2

Sol :

=164b225

=(18b)2+52

=(18b+5)(18b5)


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


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


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)

3 comments:

Contact Form

Name

Email *

Message *