Excercise =8.1
Question 1
(i) $3 x+6$
(ii) $\quad 13-5 x$
(ii) $\quad x^{2}+y^{2}$
(iv) $\quad 3 p q+7$
(v) $\quad x^{2}-3 x$
ii) $\quad mn-(m+n)$
Question 2
A taxi charges = 9\km
fixed charges = 80
Taxo fixed for x km is
9x + 50
Question 3
(i) $\quad 5 a-3 b+c$
(ii. $\quad x^{2}-5 x+6 .$
(iii) $x^{2} y+x y-x y^{2}$
Question 4
(i) $3,-7 x$
ii. $2,-5 a, \frac{3}{2} b$
iii, $3 x^{5}, 4 y^{3},-7 x y^{2}, 3$
Question 5
i) -4x + 5y
Term - 4x , 5y
Factor -4x 5y
ii) $\quad x y+2 x^{2} y^{2}$
Term $: x y \quad, \quad 2 x^{2} y^{2}$
'
factor: $x, y \quad 2, x, x, y, y$
iii) $1.2 a b-2.4 b+3.6 a$
Term $: 1.2 a b \quad-2.4 b \quad 3.6 a$
farror : $1.2, a, b \quad-2.4, b \quad 3.6, a$
Question 6
i) $8 x+3 y^{2}$
(to be added)
ii)$y-y^{3}$
(to be added)
iii) $5 x y^{2}+7 x^{2} y$
(to be added)
iv) $-a b+2 b^{2}-3 a^{2}$
(to be added)
Question 7
i) $-7$
ii) $-2$
iii) 6
iv) $2 / 3$
Question 8
i) $-4 b$
ii) $5 y_{2}$
iii) $-1$
iv) $-3 x y$
Question 9
i) $-y^{2} z^{3}$
ii) $72^{3}$
(iii) $-7 y z^{2}$
iv) $-x y z$
Question 10
i) Non - constant term = -7x
Numerical coefficients = -7
ii) $1+2 x-3 x^{2}$
Non-constant term $2 x,-3 x^{2}$
Numerical coefficients $=2,-3$
iii) 1.2a + 0.8 b
Non- constant term = 1.2a , 0.8b
Numerical coefficient = 1.2, 0.8
Question 11
(i) $13 y^{2}-8 x y$
$-8 x y$
coefficient of $x=-8 y$
ii) 7x - $x y^{2}$
$7 x,-x y^{2}$
Coefficient of x = 7 $-y^{2}$
(iii)
$\begin{aligned} 5 &-7 x y z+4 x^{2} y \\ &-7 x y z, 4 x^{2} y \end{aligned}$
Coefficient of x = -7xyz , 4xy
Question 12
i)
$\begin{aligned} 8-x y^{2} \\-& x y^{2} \end{aligned}$
Coefficient of $y^{2}=-x$
ii)
$\begin{aligned} 5 y^{2} &+7 x-3 x y^{2} \\ & 5 y^{2},-3 x y^{2} \end{aligned}$
Coefficient of $y^{2}=5,-3 x$
iii)
$\begin{aligned} 2 x^{2} y &-15 x y^{2}+7 y^{2} \\-& 15 x y^{2}, 7 y^{2} \end{aligned}$
Coefficient of $y^{2}=-15 x^{2}, 7$
Question 13
i) 4y-72 binomial
ii) $-5 x y^{2}$ monomial
iii) $x+y-x y \quad$ trinomial
iv) $a b^{2}-5 b-3 a$ trinomial
v) $4 p^{2} q-5 p q^{2} \quad$ binomial
(vi) 2017 monomial
(vii) $1+x+x^{2}$ trinamial
(viii) $5 x^{2}-7+3 x+4$ trinomial
Question 14
i) $-7 x, 5 / 2^{x}$ Like term
ii) $-29 x,-29 y$ unlike term
iii) $2 \mathrm{xy}, 2 \mathrm{xy} 2$ unlike term
iv) $4 m^{2} p, 4 m p^{2}$ unlike term
v) $\quad 12 x z, 12 x^{2} z^{2}$ unlike term
vi) $-59 q, 79 p$ like term
Question 15
i) $x^{2} y,-2 x^{2} y$
ii) $3 a^{2} b,-6 x^{2} b, 2 a b c$, 4abc
iii) $10 p q,-7 p q, 78 q p .$
$7P,2405 P .$
$8 q,-100 q$
$-p^{2} q^{2}, 12 q^{2} p^{2}$
$-23,41$
$-5 p^{2}, 701 p^{2}$
$13 p^{2} q, q p^{2}$
Question 16
ii, 8
ii, 1
iii, 0
iv, 2
Question 17
$\begin{array}{ll}\text { (i) } & 3 \\ \text {(ii)} & 4 \\ \text ({iii)} 5\end{array}$
Question 18
i) True
ii) False
iii) False
iv) False
v) True
vi) False
vii) False
Excercise =8.2
Question 1
i)
$\begin{aligned} 7 x,-3 x & \\ 7 x-3 x &=4 x \end{aligned}$
ii) $6 x,-11 x$
$6 x-11 x=-5 x$
iii) $5 x^{2},-9 x^{2}$
$5 x^{2}-9 x^{2}=-4 x^{2}$
iv) $3 a b^{2},-5 a b^{2}$
$3 a b^{2}-5 a b^{2}=-4 a b^{2}$
v) $\frac{1}{2} p q,-1 / 3 p q$
$=\frac{1}{2} p q-\frac{1}{3} p q$
$=\frac{3 p q-2 p q}{3 \times 2}$
$=\frac{p q}{6}$
vi)$5 x^{3} y,-\frac{2}{3} x^{3} y$
$=5 x^{3} y-\frac{2}{3} x^{3} y$
$=\frac{15 x^{3} y-2 x^{3} y}{3}$
$=\frac{13 x^{3} y}{3}$
Question 2
i)
$\begin{aligned} 3 x-5 x, 7 x & \\ 3 x-5 x+7 x=5 x \end{aligned}$
ii) 7xy, $2 x y$, $-8 x y$
=$27 x y+2 x y-8 x y$
=xy
iii) $-2 a b c, 3 a b c, a b c$
$-2 a b c+3 a b c+a b c=2 a b c$
iv) $3 m n,-5 m n, 8 m n,-4 m n$
$3 m n-5 m n+8 m n-4 m n=2 m n$
v) $2 x^{3}, 3 x^{3},-4 x^{3},-5 x^{3}$
$2 x^{3}+3 x^{3}-4 x^{3}-5 x^{3}$
$5 x^{3}-9 x^{3}=-4 x^{3}$
Question 3
i) $8 b-32$
ii) $8 m^{2}-11 m+10$
iii) $7 z^{3}+12 z^{2}-202$
iv) $8 x^{2} y+$ 8xy $^{2}-4 x^{2}-7 y^{2}$
v) p-q
vi) $\quad a+a b$
vii) $ \quad 4 y^{2}-3 y$
Question 4
i) $5 x y,-7 x y, 3 x^{2}$
=$5 x y-7 x y+3 x^{2}$
=$3 x^{2}-2 x y$
ii) $4 x^{2} y_{2}-3 x y^{2},-8 x y^{2}, 5 x^{2} y$
=$4 x^{2} y-3 x y^{2}-5 x y^{2}+5 x^{2} y$
=$9 x^{2} y-8 x y^{2}$
iii) $-7 m n+5,12 m n+12,8 m n-8,-2 m n-3$
=$-7 m n+5+18 m n+12+8 m n-8-2 m n-3$
=$11 m n-4$
iv) $a+b-3, \quad b-a+3, a-b+3$
=$a+b-3+b-a+3+a-b+3$
=$\quad a+b+3$
v) $14 x+10 y-12 x y-13, \quad 18-7 x-10 y+8 x y, 4 x y$
=$14 x+10 y-12 x y-13+18-7 x-10 y+8 x y+4 x y$
=$7 x+5$
vi) $5 m-7 n, \quad 3 n-4 m+2,2 m-3 m n-5$
=$5 m-7 n+3 n-4 m+2+2 m-3 m n-5$
=$3 m-4 n-3 m n-3$
vii)$7 a^{2}-5 a+2, \quad 3 a^{2}-7, \quad 2 a+a, \quad 1+2 a-5 a^{2}$
=$7 a^{2}-5 a+2+3 a^{2}-7+2 a+9+1+2 a-5 a^{2}$
=$5 a^{2}-a+5$
Question 5
i) $2 x^{2}+3 y^{2}-5 x y+5 x^{2}-y^{2}+6 x y-3 x^{2}$
=$x^{2}(2+3)+y^{2}(3-1)+x y(-5+6)$
=$4 x^{2}+2 y^{2}+x y$
ii) $3 x y^{2}-5 x^{2} y+7 x y-8 y^{2} x-4 x y+6 x^{2} y$
=$x y^{2}(3-8)+x^{2} y(-5+6)+x y(7-4)$
=$-5 x y^{2}+6 x^{2} y+3 x y$
iii) $5 x^{4}-7 x^{2}+8 x-1+3 x^{3}-9 x^{2}+7-3 x^{4}+11 x-2+8 x^{2}$
=$x^{4}(5-3)+x^{2}(-7-9+8)+x(8+11)+3 x^{3}-1+7-2$
=$2 x^{4}-8 x^{2}+19 x+3 x^{3}+4$
=$2 x^{4}+3 x^{3}-8 x^{2}+19 x+4$
Question 6
i) $y^{2}-\left(-5 y^{2}\right)$
$y^{2}+5 y^{2}=6 y^{2}$
ii) $-2 x y-(-7 x y)$
$-2 x y+7 x y$
$5 x y$
iii) $b(5-a)-a(b-5)$
$5 b-a b-a b+5 a$
$5 a+5 b-2 a b$
iv) $4 m^{2}-3 m n+8-\left(-m^{2}+5 m n\right)$
$4 m^{2}-3 m n+8+m^{2}-5 m n$
$5 m^{2}-8 m n+8$
v)$3 a b-2 a^{2}-2 b^{2}-\left(5 a^{2}-7 a b+5 b^{2}\right)$
$3 a b-2 a^{2}-2 b^{2}-5 a^{2}+7 a b-5 b^{2}$
$10 a b-7 a^{2}-7 b^{2}$
vi) $5 p^{2}+3 q^{2}-p q-\left(4 p q-5 q^{2}-3 p^{2}\right)$
$5 p^{2}+3 q^{2}-p q-4 p q+5 q^{2}+3 p^{2}$
$8 p^{2}+8 q^{2}-5 p q$
vii) $7 x^{2}-8 x y+3 y^{2}-5-\left(7 x y+5 x^{2}-7 y^{2}+3\right)$
$7 x^{2}-8 x y+3 y^{2}-5-7 x y-5 x^{2}+7 y^{2}-3$
$x^{2}(7-5)+x y(-8-7)+y^{2}(3+7)-8$
$2 x^{2}-15 x y+10 y^{2}-8$
viii) $\left(x^{4}-3 x^{3}-2 x^{2}+3\right)-\left(2 x^{4}-7 x^{2}+5 x+3\right)$
$x^{4}-3 x^{3}-2 x^{2}+3-2 x^{4}+7 x^{2}-5 x-3$
$x^{4}(1-2)-3 x^{3}+x^{2}(-2+7)-5 x$
$-x^{4}-3 x^{3}+5 x^{2}-5 x$
Question 7
Sum of ( 10p - r ) and 5P+ 2q is
$=10 p- r+5 p+2 q$
=$15 p+2 q-r$
$P-2 q+r$ Subtract from $15 p+2 q-r$
=$(15 p+2 q-r)-(p-2 q+r)$
=$15 p+2 q-r-p+2 q-r$
=$p(15-1)+q(2+2)+r(-1-1)$
=$14 p+4 q-2 r$
Question 8
Sum of $4+3 x$ and $5-4 x+2 x^{2}$
$2 x^{2}-4 x+5+4+3 x$
$2 x^{2}-x+9$
Sum of $3 x^{2}-5 x$ and $-x^{2}+2 x+5$
=$3 x^{2}-5 x+\left(-x^{2}+2 x+5\right)$
=$2 x^{2}-3 x+5$
$2 x^{2}-x+9$ is substracted from $2 x^{2}-3 x+5$
=$2 x^{2}-3 x+5-\left(2 x^{2}-x+9\right)$
=$2 x^{2}-3 x+5-2 x^{2}+x-9$
=$2x-4$
Question 9
Sum is $x^{2}+y^{2}+5 x y$
Subtract $x^{2}-y^{2}+2 x y$ from $x^{2}+y^{2}+5 x y$
$x^{2}+y^{2}+5 x y$
$x^{2}-y^{2}+2 x y$
$-$ $+$ $-$
---------------------------------
$2 y^{2}+3 x y$
Question 10
$-7 m n+2 m^{2}+3 n^{2}$
$2 m n+m^{2}+n^{2}$
$-$ $-$ $-$
------------------------------------
$-9 m n+m^{2}+2 n^{2}$
Question 11
The required
$y^{4}-12 y^{2}+y+14-\left(17 y^{3}+34 y^{2}-51 y+68\right)$
$y^{4}-17 y^{3}+y^{2}(-12-34)+y(1+51)+14-68$
$y^{4}-17 y^{3}-46 y^{2}+52 y-54$
Question 12
The required
$93 p^{2}-55 p+4-\left(13 p^{3}-5 p^{2}+17 p-90\right)$
$93 p^{2}-55 p+4-13 p^{3}+5 p^{2}-17 p+90$
$-13 p^{3}+98 p^{2}-72 p+94$
Question 13
The required expressions
$3 x^{2}-4 y^{2}+5 x y+20$
$-x^{2}-y^{2}+6 x y+20$
$+$ $+$ $-$ $-$
-------------------------------------
$4 x^{2}-2 y^{2}-x y$
Question 14
Sum of $2 y^{2}+3 y z,-y^{2}-y z-z^{2}, \quad y z+2 z^{2}$ is
$2 y^{2}+3 y z-y^{2}-y z-z^{2}+y z+2 z^{2}$
$y^{2}(2-1) 7 y z(3-1+1)+z^{2}(-1+2)$
$y^{2}+3 y z+z^{2}$
Excercise =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
Excercise =8.4
Question 1
i) $2 n+1$
Number of shapes
1
2
3
No of Line segments
3
5
7
n shape of letter are formed then algrabraic equation is 2n + 1
ii) Number of shapes
1
2
3
No, of line segments
5
8
11
Algrebraic equation is 3n + 2
Question 2
i) Number of shapes
1
2
3
$\vdots$
No, of line segments
4
7
10
$\vdots$
Alegebraic expression is 3nm
ii) Number of shapes
1
2
3
No. of line segments
6
11
16
Algebraic expression is 5n + 1
iii) Number of shapes
1
2
3
No. of line segments
7
12
17
Algebraic expression is 5n+ 2
Question 3
i) $2 n+1$
$n=5 \quad 2(5)+1=11$
$n=10 \quad 2(10)+1=21$
$n=100 \quad 2(100)+1=201$
ii) $3 n+1$
$n=5 \quad 3(5)+1=16$
$n=10 \quad 3(10)+1=31$
$n=100 \quad 3(100)+1=301$
iii) $3 n+2$
$n=5 \quad 3(5)+2=17$
$n=10 \quad 3(10)+2=32$
$n=100 \quad 3(100)+2=302$
iv) $n=5(5)+1=26$
$n=10 \quad 5(10)+1=51$
$n=100 \quad 5(100)+1=501$
v) $5 n+2$
$n=5 \quad 5(5)+2=27$
$n=10 \quad 5(10)+2=52$
$n=100 \quad 5(100)+2=502$
vi) $4 n+3$
$n=5 \quad 4(5)+3=23$
$n=10 \quad 4(10)+3=43$
$n=100 \quad 4(100)+3=403$
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