myhelper: 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:

$\frac{x^{2} - 5 x + 6}{x - 3} = \frac{x^{2} - 3 x - 2 x + 6}{x - 3} = \frac{x (x - 3) - 2 (x - 3)}{(x - 3)} = \frac{(x - 3) (x - 2)}{(x - 3)} = x - 2$

Question 2:

Divide:
ax² − ay² by ax + ay

Answer 2:

$\frac{a x^{2} - a y^{2}}{a x + a y} = \frac{a (x^{2} - y^{2})}{a (x + y)} = \frac{a (x + y) (x - y)}{a (x + y)} = x - y$

Question 3:

Divide:
x⁴ − y⁴ by x² − y²

Answer 3:

$\frac{x^{4} - y^{4}}{x^{2} - y^{2}} = \frac{(x^{2})^{2} - (y^{2})^{2}}{(x^{2} - y^{2})} = \frac{(x^{2} + y^{2}) (x^{2} - y^{2})}{(x^{2} - y^{2})} = x^{2} + y^{2}$

Question 4:

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

Answer 4:

$\frac{a c x^{2} + (b c + a d) x + b d}{(a x + b)} = \frac{a c x^{2} + b c x + a d x + b d}{(a x + b)} = \frac{c x (a x + b) + d (a x + b)}{(a x + b)} = \frac{(a x + b) (c x + d)}{(a x + b)} = c x + d$

Question 5:

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

Answer 5:

$\frac{(a^{2} + 2 a b + b^{2}) - (a^{2} + 2 a c + c^{2})}{(2 a + b + c)} = \frac{(a + b)^{2} - (a + c)^{2}}{(2 a + b + c)} = \frac{(a + b + a + c) (a + b - a - c)}{(2 a + b + c)} = \frac{(2 a + b + c) (b - c)}{(2 a + b + c)} = b - c$

Question 6:

Divide:
$\frac{1}{4} x^{2} - \frac{1}{2} x - 12 by \frac{1}{2} x - 4$

Answer 6:

$\frac{\frac{1}{4} x^{2} - \frac{1}{2} x - 12}{\frac{1}{2} x - 4} = \frac{\frac{1}{2} x (\frac{1}{2} x - 4) + 3 (\frac{1}{2} x - 4)}{\frac{1}{2} x - 4} = \frac{(\frac{1}{2} x - 4) (\frac{1}{2} x + 3)}{(\frac{1}{2} x - 4)} = \frac{1}{2} x + 3$

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