ML AGGARWAL CLASS 8 CHAPTER 10 Algebraic Expressions and Identities Exercise 10.4

 Exercise 10.4

Question 1

Sol :

(i) $-39 p q^{2} r^{5} \div-24 p^{3} q^{3} r$

$=\frac{-39 p q^{x}+5}{-24 p^{3} q^{3} r}$

$\frac{13 \cdot r^{4}}{8 p^{2} q}$

(ii) $-\frac{3}{4} a^{r} b^{3} \div \frac{6}{7} a^{3} b^{2}$

=$\frac{\frac{-3}{4} a^{2} b^{3}}{\frac{6}{7} a^{3} b^{2}}$

$=\frac{-3}{4} \times \frac{7}{6}-\frac{b}{a}$

$=\frac{-7 b}{8 a}$

Question 2

Sol :

(i)

$3 x^{3}-\frac{8}{3} x^{2}-4$

$\begin{array}{l}3 x \sqrt{9 x^{4}-8 x^{3}-12 x+3} \\\frac{\left(-9 x^{4}\right.}{0-8 x^{3}} \\\frac{(+)^{-8 x^{3}}}{0-12 x} \\\frac{\frac{1-12 x}{}}{0+3}\end{array}$

Quotient $=3 x^{3}-\frac{8}{3} x^{2}-4 ;$ Remainder $=3$

(ii) 

Quotient =3 x+5,  Remainder =0

Question 3

Sol :

(i) 

Quotient =3 x+5 , Remainder =0

(ii)  

Quotient $=y^{2}$-y-1 Remainder =2

(iii) 

Quotient =-2 x+3, Remainder =2

(iv)  

Quotient = $x^{2}-4 x+4$, Remainder =0

Question 4

Sol :

(i) 

Quotient $=2 x^{2}+5 x+3$, 

Remainder =-4

(ii) 

Quotient $=m^{2}-5 m-5$, 

Remainder =2

Question 5

Sol :

(i) 

Quotient =a+1, Remainder =0

(ii)  

Quotient =4 x-3, Remainder =-3

Question 6

Sol :

Given area of rectangle = $8 x^{2}-45 y^{2}+18 x y$

one side $S_{1}=4 x+15 y$

other side $\quad S_{2}=?$

$A=S_{1} \times S_{2}$

$S_{2}=A \div S_{1}$

Quotient =2 x-3 y, Remainder =0

∴ length other side of rectangle 

$s_{2}=2 x-3 y$