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

 Exercise 6B 

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Q1 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 1

Add: 

(i) 2x, 3x, x, 5x

Sol: 

=2x+3x+x+5x

=11x

 

(ii) 8m, 3m, 4m , 2m 

Sol: 

=8m+3m+4m+2m

=17m

(iii) $-3 b^{2}, 5 b^{2}$

Sol: 

$=-3 b^{2}+5 b^{2}$

$=2 b^{2}$

(iv) -7x, 2x, 4x ,-x

Sol: 

=-7x+2x+4 x+(-x)

=-7x+2x+4x-x

=-8 x+6x=-2x

(v) -x ,-x, -x

Sol: 

=-x +(-x)+ (-x)

=-x-x-x 

=-3x

(vii) $4 b x^{2},-9 b x^{2} .$

Sol: 

$=4 b x^{2}+\left(-9 b x^{2}\right)$

$=4 b x^{2}-9 b x^{2}$

$=-5 b x^{2}$

(v) 0, y 

Sol: 

0+y = y

(viii) $\frac{1}{2} ax, \frac{1}{2}ax$

Sol : 

$=\frac{1}{2} a x+\frac{1}{2} a x$

$1a x=a x$

(ix) 2y, -5y ,6y, -4y

Sol: 

=2y+(-5y)+6y+(-4y)

=2y-5y+6y-4y

=8y-9y=-y

(x) -9xy, -xy

Sol : 

=-9xy+(-xy)

=-9xy-xy

=-10xy

(xi) 0,$-7 b^{2} y^{2}$

Sol :

$=0+\left(-7 b^{2} y^{2}\right)$

$=-7 b^{2} y^{2}$

(xii)  $-6 a^{4} b^{2} x^{2}+6 a^{4} b^{2} z_{1}^{2}$

Sol: 

$=-6 a^{4} b^{2} x^{2}+6 a^{4} b^{2} x^{2}$

=0

(xiii) $a b^{3} c,-2 a b^{3} c,-2 a b^{3} c$

Sol: 

$=a b^{3} c+\left(-2 a b^{3} c\right)+\left(-2 a b^{3} c\right)$

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

$=a b^{3} c-4 a b^{3} c=-3 a b^{3} c$

(xiv) 6(a+b), 3(a+b)

Sol: 

$=6(a+b)+3(a+b)$

$=6 a+6 b+3 a+3 b$

$=9 a+9 b=9(a+b)$

(xv) 2a, 3b, 4c

Sol :

= 2a+3b+4c

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Q2 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 2

Simplify: 

(i) e+e+e+e+e+e+e

Sol: 7e

(ii) $3 p+p-p+p-p$

Sol:$3 p$

(iii) $k+3 k-2 k+7 k-5 k$

Sol: $=11 k-7 k .$

$=4 k$

(iv) 8$r^{3}$ - $10 r^{3}+6 r^{3}$

Sol: $=14 r^{3}-10 r^{3}$

$=4 r^{3}$

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Q3 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 3

(i)  

$\begin{aligned}&6 a+4 b \\&2 a+5 b \\&\hline 8 a+9 b \\&\hline\end{aligned}$

(ii)

$\begin{aligned}&2 x+5 y \\&\frac{3 x+y}{4 x+6 y}\end{aligned}$

(iii)

$\begin{array}{r}5 t-1 \\-6 t+4 \\\hline-t+3 \\\hline\end{array}$

(iv) 

$\begin{aligned}&3 a+b \\&a-b \\ \hline&4 a \\\hline\end{aligned}$

(v)

$\begin{array}{r} x^{2}+2 \\-6 x^{2}+3 \\\hline-5 x^{2}+5 \\\hline\end{array}$

(vi) 

$\begin{array}{r}-6x-2 \\-x-5 \\\hline-7x-7 \\\hline\end{array}$

(vii)

$\begin{aligned}&3 a b-9xy \\&7 a b+4xy \\\hline &10 a b-5x y \\\hline\end{aligned}$

(viii) 

$\begin{aligned}&-c^{2}+5 c \\&\frac{-4 c^{2}+8 c}{-5 c^{2}+13 c} \\\hline\end{aligned}$

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Q4 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 4

(i)

$\begin{aligned}&2 a+3 b+1 \\&\frac{4 a+2 b+7}{6 a+5 b+8}\end{aligned}$

(ii)

$\begin{aligned}&x^{2}+2 x-7 \\ &x^{2}-5 x+3 \\\hline &2 x^{2}-3x-4\end{aligned}$

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Q5 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 5

(i)

$\begin{array}{r}3 a-4 b \\7 a-2 b \\-2 a+b \\\hline 8 a-5 b \\\hline\end{array}$

(ii)

$\begin{gathered}a^{2}-6 \\-4 a^{2}+2 \\-7 a^{2}+5 \\\hline-10 a^{2}-1 \\\hline\end{gathered}$

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Q6 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 6

(i) $\begin{array}{r}x^{2}-3 x+4 \\4 x^{2}-2 x+7 \\-x^{2}+5 x-2 \\ \hline4x^{2}+0+9 \\\hline\end{array}$

(ii) $\begin{aligned}x^{3}+6x^{2}\phantom{+3x-7~~}&\\5x^{2}+3x\phantom{+5x}&\\5x-7& \\ \hline x^{3}+11x^{2}+8x-7 \\\hline\end{aligned}$

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Q7 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 7

(i) $\left(c^{2}+2cd)+(-3 c d-d^{2}\right)$

Sol:

$=c^{2}+2 c d-3 c d-d^{2}$

$=c^{2}-c d-d^{2}$

(ii) $(x-6)+(3 x-4)+(x-1)$

Sol: 

$=x-6+3 x-4+ x-1$

$=5 x-11$

(iii) $3 m n^{2}+4 m^{2} n^{2}+\left(-5 m n^{2}\right)+\left(-m n^{2}\right)$

Sol: 

$=3 m n^{2}+4 m^{2} n^{2}-5 m n^{2}-m n^{2}$

$=4 m^{2} n^{2}+3 m n^{2}-6 m n^{2}$

$=4 m^{2} n^{2}-3 m n^{2}$

(iv) $(x-y)+(y-x)+(2 y-x)$

Sol: 

=x-y+y-x+2y-x

= 2y-x

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Q8 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 8  

Match the expression in column A to the sum in column B

 

(i) $3 x^{2}+5 x-4+6 x^{2}-x+7$ (ii) $2 y^{2}-3 y+6+y^{2}-5 y-1+(-4)+2 y^{2}-2 y$ (iii) $2 x^{2} y-3 x y^{2}+x^{2} y-4 x^{2} y-2 x y^{2}$ (iv) $x^{2}-y^{2}+2 x^{2}-3 x y+4 y^{2}+3 y^{2}-5 x y-x^{2}$

(A) $5 y^{2}-10 y+1$ (B) $2 x^{2}-8 x y+6 y^{2}$ (C) $9 x^{2}+4 x+3$ (D) $-x^{2} y-5 x y^{2}$

Sol :

(i) - (C)

(ii) - (A)

(iii) - (D)

(iv) - (B)

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Q9 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 9

 

If P= $2 y^{2}-5-2 y$ , Q= $y^{2}-3 y+6$ and R = $y^{2}-4 y+2$ Find  P+2Q+2R

Sol:  

$=2 y^{2}-5-2 y+2 \times\left(y^{2}-3 y+6\right)+2 x\left(y^{2}-4 y+2\right)$

$=2 y^{2}-5-2 y+2 y^{2}-6 y+12+2 y^{2}-8 y+4$

$=6 y^{2}-16 y+11$

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Q10 | Ex-6B | Class 7 | Algebraic Expression | S.Chand |Composite Mathematics |Chapter 6 |myhelper

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Question 10

Find the perimeter of triangle 

Sol: 

$=A B+B C+A C$

$=3x-7+2x+5+(-x+11)$

$=3x-7+2x+5-x+11$

$=4x+9$