ML AGGARWAL CLASS 7 Chapter 8 Algebraic Expressions Exercise 8.3

 Exercise 8.3

Question 1

i. $3 m-5$

Given $m=2$

$\quad 3(2)-5=6-5=1$

ii) $9-5 m$

$m=2$

$9-5(2)=9-10$

$=-1$

iii, $3 m^{2}-2 m-7$

$m =2$

$3(2)^{2}-2(2)-7$

$3 \times 4-2 \times 2-7$

$12-4-7$

= 1 Ans

iv) $\frac{5}{2} m-4$

$m=2$

=$\frac{5}{2} \times 2-4$

$5-4$ = 1

Question 2

i)

 $\begin{aligned} 4 p+7 & \\ p &=-2 \\ & 4(-2)+7=-8+7=-1 \end{aligned}$

ii) $-38^{2}+4 p+7$

$-3(-2)^{2}+4(-2)+7$

$-3 \times 4-8+7$

$-12-8+7$

$-13$

iii) $-2 p^{3}-3 p^{2}+4 p+7$

=$-2 x(-2)^{3}-3(-9)^{2}+4(-2)+7$

=$-2 x-8-3 \times  4+4 x-2+7$

=$16-12-8+7$

=3

Question 3

(i) $a^{2}+b^{2}$

$a=2, b=2$

$(2)^{2}+(2)^{2}$

$4+4=8$

ii) $a^{2}+a b+b^{2}$

$a=2 \quad b=2$

$(2)^{2}+2 x a+(2)^{2}$

=$4+4+4$

$=12$

iii) $a^{2}-b^{2}$

=$(2)^{2}-(2)^{2}$

=$4-4$

=0

Question 4

i) $2 a^{2}+b^{2}+1$

$a=0 \quad b=-1$

=$2 \times(0)^{2}+(-1)^{2}+1$

=$0+1+1$

=2

ii) $a^{2}+a b+2$

=$(0)^{2}+0 \times -1+2$

=0

iii) $2 a^{2} b+2 a b^{2}+a b$

=$2(0)^{2}(-1)+2(0)(-1)^{2}+0(-1)$

= 0

Question 5

Given $p=-10$

The value of $p^{2}-2 p-100$

=$(-10)^{2}-2(-10)-100$

=$100+20-100$

=20

Question 6

Given = 10

The value of $z^{3}-3 z+30$

=$(10)^{3}-3(10)+30$

=$1000-30+30$

=1000

Question 7

Given x = 2

The value of $x+7+4(x-5)$ is

$x+7+4 x-20$

$5 x-13$

$5 \times 2-13$

$10-13=-3$

ii) Given $x=2$

The value of $3(x+2)+5 x-7$

=$3 x+6+5 x-7$

=$8 x-1$

=$8(+2)-1$

=$16-1$

=15

iii) Given x = 2

The value of $6 x+5(x-2)$

=$6 x+5 x-10$

=$11 x-10$

=$11 \times 2-10$

=$22-10$

=12

iv) Given x = 2

The value of $4(2 x-1)+3 x+11$

=$8 x-4+3 x+11$

=$11 x+7$

=$11 \times 2+7$

=$22+7$

= 29

Question 8

(i) Given a=-1, b=-2

=$2 a-2 b-4-5+a$

=$2(-1)-2(-2)-4-5+(-1)$

=$-2+4-4-5-1$

=$-8$

ii) Given $a=-1, \quad b=-2$

The value of $2\left(a^{2}+a b\right)+3-a b$

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

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

=$2(-1)^{2}+(-1)(-2)+3$

=$2+2+3$

=7