Exercise 6B
Question 1
Add:
(i) $2 x, 3 x, x,5x$
Sol: $2 x+3 x+x+5 x$
$11 x$
(ii) 8m, 3m, 4m , 2m
Sol: $8 m+3 m+4 m+2 m$
$17 m$
(iii) $-3 b^{2}, 5 b^{2}$
Sol: $-3 b^{2}+5 b^{2}$
$2 b^{2}$
(iv) $-7 x, 24, 4x ,-x$
Sol: $=-7 x+2 x+4 x+(-x)$
$=-7 x+2 x+4 x-x$
$=-8 x+6 x$
$-2 x$
(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: $=2 y+(-5 y)+6 y+(-4 y)$
$=2 y-5 y+6 y-4 y$
$=8 y-9 y=-y$
(x) -9xy, -xy
Sol: -9xy+(-xy)
=-9xy-xy
=-10xy
(xi) 0,$-7 b^{2} y^{2}$
$=0+\left(-7 b^{2} y^{2}\right)$
$=-7 b^{2} y^{2}$
(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
= 2a+3b+4c
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: $=14 r^{3}-10 r^{3}$
$=4 r^{3}$
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) (TO BE ADDED)
(v)
$\begin{array}{r}2 x^{2}+2 \\-6 x^{2}+3 \\\hline-5 x^{2}+5 \\\hline\end{array}$
(vi)
$\begin{array}{r}-6x-2 \\-x-5 \\\hline-7x-7 \\\hline\end{array}$
(vii) (To be added)
(viii) (To be added)
Question 4
(i)
$\begin{aligned}&2 a+3 b+1 \\&\frac{4 a+2 b+7}{6 a+5 b+8}\end{aligned}$
(ii)
$\begin{gathered}x^{2}+2 x-7 \\x^{2}-5 x+3 \\\hline 2 x^{2}-3x-4\end{gathered}$
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)
$\begin{gathered}a^{2}-6 \\-4 a^{2}+2 \\-7 a^{2}+5 \\\hline-10 a^{2}-1 \\\hline\end{gathered}$
Question 6
(i) (TO BE ADDED)
(ii) (TO BE ADDED)
Question 7
(i) $\left(c^{2}+2(d)\right)+\left(-3 (d-d^{2}\right)$
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: $x-y+y-x+2 y-x$
= 2y-x
Question 8
(To be added)
Question 9
If P= $2 y^{2}-5-2 y$ , Q= $y^{2}-3 y+6$ and R = $y^{2}-4 y+2$ Find $p+2 Q+2 R$
Sol: $=2 y^{2}-5-2 y+2 \times\left(y^{2}-3 y+6\right)+2 x\left(y^{2}-4 y+2\right)$
$=2 y^{2}-5-2 y+2 y^{2}-6 y+12+2 y^{2}-8 y+4$
$=6 y^{2}-16 y+11$
Question 10
Find the perimeter of triangle
(Figure to be added)
Sol: $=A B+B C+A C$
$=3x-7+2x+5+(-x+11)$
$=3x-7+2x+5-x+11$
$=4x+9$
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