RD Sharma solution class 8 chapter 8 Division of Algebraic Expression Exercise 8.6

Exercise 8.6

Page-8.17

Question 1:

Divide:
x2 − 5x + 6 by x − 3

Answer 1:

x2-5x+6x-3=x2-3x-2x+6x-3=x(x-3)-2(x-3)(x-3)=(x-3)(x-2)(x-3)= x-2

Question 2:

Divide:
ax2ay2 by ax + ay

Answer 2:

ax2-ay2ax+ay=a(x2-y2)a(x+y)=a(x+y)(x-y)a(x+y)= x-y

Question 3:

Divide:
x4y4 by x2y2

Answer 3:

 x4-y4x2-y2=(x2)2-(y2)2(x2-y2)=(x2+y2)(x2-y2)(x2-y2)= x2+y2

Question 4:

Divide:
acx2 + (bc + ad)x + bd by (ax + b)

Answer 4:

acx2+(bc+ad)x+bd(ax+b)=acx2+bcx+adx+bd(ax+b)=cx(ax+b)+d(ax+b)(ax+b)=(ax+b)(cx+d)(ax+b)= cx+d

Question 5:

Divide:
(a2 + 2ab + b2) − (a2 + 2ac + c2) by 2a + b + c

Answer 5:

(a2+2ab+b2)-(a2+2ac+c2)(2a+b+c)=(a+b)2-(a+c)2(2a+b+c)=(a+b+a+c)(a+b-a-c)(2a+b+c)=(2a+b+c)(b-c)(2a+b+c)=b-c

Question 6:

Divide:
14x2-12x-12 by 12x-4

Answer 6:

14x2-12x-1212x-4=12x(12x-4)+3(12x-4)12x-4=(12x-4)(12x+3)(12x-4)=12x+3

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