ML AGGARWAL CLASS 8 CHAPTER 10 Algebraic Expressions and Identities Exercise 10.1

 Exercise 10.1

Question 1

Sol :

(i)  Given expression $12 x^{2} y z-4 x y^{2}$

Terms         

         

$12 x^{N} y z$

$-4 x y^{2}$

Numerical coefficient 

12 , -4

Literal Coefficient 

$x^{2} y z$

$x y^{2}$

(ii) Given expression $8+m n+n l-1 m$

Terms

8mn , nl  ,-lm

Numerical cofficient 

8 ,1 , 1 ,-1

Literal Coefficient 

- ,mn  ,nl ,lm

(iii) Given expression $\frac{x^{2}}{3}+\frac{4}{6}-x y^{2}$

Terms

$\frac{x^{2}}{3}$

$\frac{y}{6}$

$-x y^{2}$

Numerical co-efficient 

$\frac{1}{3}$

$\frac{1}{6}$

-1

Literal co - efificient

$x^{2}$

$y$

$x y^{2}$

(iv) Given expression $-4 p+2.3 q+1.7 r$

Terms

$-4 \mathrm{P}$ ,2.3q ,$1.7 \mathrm{r}$

Numerical co-efficient

-4 ,2.3 ,1.7

Literal co-efficient

P ,q ,r

Question 2

Sol :

(i) $5 \mathrm{p} \times \mathrm{q} \times \mathrm{r}^{2} \rightarrow$ Monomial

(ii) $3 x^{2} \times y \div 2 z \rightarrow$ Monomial

(iii) $-3+7 x^{2} \rightarrow$ Binomial

(iv) $\frac{5 a^{2}+3 b^{2}+c}{2} \rightarrow$ Trinomial

(v) $7 x^{5}-\frac{3 x}{y} \rightarrow$ Binomiol

(vi) $5 p \div 3 q-3 p_{x}^{2} \ q_{} \rightarrow$ Binomial

Question 3

(i) $\frac{2}{5} x^{4}-\sqrt{3} x^{2}+5 x-1$

Itis polynomial of degree 4

(ii)  $7 x^{3}-\frac{3}{x^{2}}+\sqrt{5}$

due to $-3 x^{-2}$ term, It is not called as polynomial

$\therefore$ It is Not Polynomial

(iii) $4 a^{3} b^{2}-3 a b^{4}+5 a b+\frac{2}{3}$

It is a polynomial of degree 5

(iv) $2 x^{2} y-\frac{3}{x y}+5 y^{3}+\sqrt{3}$

due to negative power in the $-3(x y)^{-1}$

$\therefore$ It is not a Polynomial

Question 4

Sol :

(i) Arrange terms for column method 

$\begin{array}{r}a b-b c \\0+b c-c a \\-a b \quad 0+c a \\\hline 0+0+0\end{array}$

$\therefore a b-b c+b c-c a+c a-a b=0$

(ii) Arrange terms in columns 

$5 p^{2} q^{v}+4 p q+7$

$-2 p^{2} q^{2}+9 p q+3$

---------------------------------

$3 p^{v} q^{2}+13 p q+10$

(iii) Arrange terms in columns 

$l^{2}+m^{2}+n^{2}+0+0+0$

$0+0+0+\operatorname{lm}+m n+0$

0+0+0+0+m n+nl

0+0+0+1 m+0+n l

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$l^{2}+m^{2}+n^{2}+2l m+2 m n+2 n l$

(iv) Arrange terms in columns 

$4 x^{3}-4 x^{2}+0 x+9$

$^{}+3 x^{2}+5 x+4$

$7 x^{3}+0-11 x+1$

$0+6 x^{2}-13 x+0$

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$10 x^{3}+2 x^{2}-29 x+14$

Question 5

Sol :

 (i)  $\begin{array}{r}14 a-5 a b+7 b-5\\{8 a+3 a b-2 b+7}\\(-)\quad(-)\quad(+)\quad(-) \\ \hline 6 a-8 a b+9b-12 \\ \hline \end{array}$

(ii) $12 x y-3 y z-4 z x+5 x y z$

$8 x y+4 y z+5 z x+0$

$(-) \quad(-) \quad(-)\quad(-)$

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$4 x y-7 y z-9 z x+5 x y z$

(iii) $5 p_{q}^{2}-2 p q^{2}+5 p q-11 q-3 p+18$

$4 p^{2} q+3 p q^{2}-3 p q+7 q-8 p-10$

$(-) \quad(-)\quad(+) \quad(-) \quad(+)\quad(+)$

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$p^{\gamma} q-7 p q^{2}+8 p q-18 q+5 p+28$

Question 6

Sol :

Horizontal method 

$3 x^{2}+5 x y+7 y^{2}+3 \rightarrow 1$

$2 x^{2}-4 x y-3 y^{2}+7 \rightarrow(2)$

$9 x^{2}-8 x y+11 y^{2} \rightarrow(3)$

(3) $-[(1)+(2)]$

$9 x^{2}-8 x y+11 y^{2}-\left[3 x^{2}+5 x y+4 y^{2}+3+2 x^{2}-4 x y-3 y^{2}+7\right]$

$9 x^{2}-8 x y+11 y^{2}-\left[5 x^{2}+x y+4 y^{2}+10\right]$

$9 x^{2}-8 x y+11 y^{2}-5 x^{2}-x y-4 y^{2}-10$

$4 x^{2}-9 x y+7 y^{2}-10$

Question 7

Sol :

Let $3 a^{2}-5 a b-2 b^{2}-3---(1)$

$5 a^{2}-7 a b-3 b^{2}+3 a---(2)$

do (2) - (1)

$5 a^{v}-7 a b-3 b^{2}+3 a$

$3 a^{v}-5 a b-2 b^{2}+0-3$

$(-) \quad(+)\quad(+) \quad(-) \quad(+)$

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$2 a^{2}-2 a b-b^{2}+3 a+3$

Question 8

Sol :

Perimeter of triangle (p) = $7 p^{2}-5 p+11 \rightarrow(1)$

sides 

$s_{1}=p^{2}+2 p-1 \rightarrow(2)$

$s_{2}=3 p^{2}-6 p+3 \rightarrow(3)$

$S_{3}=?$

$\begin{aligned} P &=S_{1}+S_{2}+S_{3} \\ S_{3} &=P-\left(S_{1}+S_{2}\right) \end{aligned}$

$-7 p^{2}-5 p+11-\left[p^{2}+2 p-1+3 p^{2}-6 p+3\right]$

$=7 p^{2}-5 p+11-\left[4 p^{2}-4 p+2\right]$

$=7 p^{2}-5 p+11-4 p^{2}+4 p-2$

$S_{3}=3 p^{2}-p+9$

hence third side of triangle