# RD Sharma Solutions Class 8 Division Of Algebraic Expressions Exercise 8.6

## RD Sharma Solutions Class 8 Chapter 8 Exercise 8.6

Question 1: x– 5x + 6 by (x – 3)

Soln:

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

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

= $\frac{x(x-3)-2(x-2)}{x-3}$

= $\frac{(x-3)(x-2)}{x-3}$ = x-2

Question 2: ax2-ay2  by (ax+ay)

Soln:

$\frac{ax^{2}-ay^{2}}{ax+ay}$

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

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

Question 3: x4-y4 by x2-y2

Soln:

$\frac{x^{4}-y^{4}}{x^{2}-y^{2}}$

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

= $\frac{(x^{2}-y^{2})\times (x^{2}+y^{2})}{(x^{2}-y^{2})}$ = x2+y2

Soln:

$\frac{acx^{2}+(bc+ad)x+bd}{ax+b}$

= $\frac{acx^{2}+bcx+adx+bd}{ax+b}$

= $\frac{cx(ax+b)+d(ax+b)}{ax+b}$

$\frac{(ax+b)(cx+d)}{ax+b}$ = cx+d

Question 5: (a2+2ab+b2)-(a2+2ac+c2) by (2a+b+c)

Soln:

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

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

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

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

Question 6: $(\frac{1}{4}x^{2}-\frac{1}{2}x-12)\,by\,(\frac{1}{2}x-4)$

Soln:

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

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

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