SChand Composite Mathematics Class 7 Chapter 6 Algebraic Expression Exercise 6D

 EXERCISE 6D

Question 1 

Simplify:

(i) 5 x+(3 x-7) 

Sol: 5 x+3 x-7

=8 x-7

(ii) 11+(-7 a+4) 

Sol:11-7a+ 4

=15-7 a

(iii) 6 x+(-7 x-2 y) 

Sol: 6 x-7 x-2 y

=-x-2 y

(iv) 8-(3 y+4)

Sol: 8-3 y-4

=4-3 y

(v) 5 a-(4 a-3 x) 

Sol: 5 a-4 a+3 x

=a+3 x

(vi) 2 y-(3 y+2)-6+(3 y-8)

Sol: 2 y-3 y-2-6+3 y-8=2 y-16

(vii) [3c-(2c+5d)-d]

Sol: 3 c-2 c-5 d-d=c-6 d

(viii) 4 t+[3-(2 t-4)] 

Sol: 4 t+[3-2 t+4]

4 t+3-2 t+4=2 t+7

(ix) 3 x-[x-(4 x+3 y)+5 y]

Sol: 3 x-[x-4 x-3 y+5 y]

=3 x-x+4 x+3 y-5 y

=6 x-2 y

(x) {$6 x^{2}-\left(2 x^{2}-y^{2}\right)-2 y^{2}$}

Sol:  $\left\{6 x^{2}-2 x^{2}+y^{2}-2 y^{2}\right\}$

$=4 x^{2}-y^{2}$ 

(xi) -{$-2 b-(3 b+8 c)$}

Sol: $-\{-2 b-3 b-8 c\}$

= $-\{-5 b-8 c\}$

=5b+8c

(xii) $-\left(49-a^{2}\right)-5 a^{2}$

Sol: $-49+a^{2}-5 a^{2}$

$=-49-4 a^{2}$

Question 13

Evaluate the expressions given below far a= -4

(i) a+8

Sol: -4+8

=4

(ii) 6a-14

Sol: $6(-4)-14$ 

$-24-14=-38$

(iii) $7 a^{2}+7 a-20$

Sol: $7(-4)^{2}+7(-4)-20$

=$7 \times 16-28-20$

=112-48=64

 

(iv) $a^{3}+2 a^{2}-a+5$

Sol: $(-4)^{3}+2(-4)^{2}-(-4)+5$

$-64+2 \times 16+4+5$

$-64+32+9=-23$

Question 14

Given ,=-2 and n=6 ,Evaluate: 

(i) m+n 

Sol: -2+6

=4

(ii) $2 m^{2}+8 n$

Sol: $2 \times(-2)^{2}+8 \times 6$

=$2 \times 4+48$

= $8+48=56$

(iii) $m^{2}-n^{2}$ 

Sol: $(-2)^{2}-(6)^{2}$

$4-36=-32$

(iv) $3 m^{3}+2 m^{2} n+n^{3}$ 

Sol: $3(-2)^{3}+2 \times(-2)^{2} \times 6+(6)^{3}$

=$3 \times-8+2 \times 4 \times 6+216$

= $-24+43+216=240$

Question 15

Simplify the Expressions and find their values if x=2, a =-1 , b=-3

 

(i) $4 a^{2}-b^{2}+6 a^{2}-7 b^{2}$

Sol: $4 \times(-1)^{2}-(-3)^{2}+6(-1)^{2}-7(-3)^{2}$

$=4 \times 1-9+6-7 \times 9$

$=4-9+6-63$

$=-62$

(ii)  $3 x^{2}-8 a b+4 x^{2}+11 a b$

Sol:$\begin{aligned} 3(2)^{2}-8(-1)(-3) &+4(2)^{2} \\ &+11(-1)(-3\end{aligned}$

$=3 \times 4-24+4 \times 4+33$

$=12-24+16+33$

$=37$