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Algebraic Expressions And Identities
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NCERT Solutions
Algebraic Expressions And Identities
15 Solutions
Exercise:
All Exercises
EXERCISE 8.1
EXERCISE 8.2
EXERCISE 8.3
EXERCISE 8.4
Q1
EXERCISE 8.1
Add the following.
(i)
a
b
−
b
c
,
b
c
−
c
a
,
c
a
−
a
b
ab-bc, bc-ca, ca-ab
ab
−
b
c
,
b
c
−
c
a
,
c
a
−
ab
(ii)
a
−
b
+
a
b
,
b
−
c
+
b
c
,
c
−
a
+
a
c
a-b+ab, b-c+bc, c-a+ac
a
−
b
+
ab
,
b
−
c
+
b
c
,
c
−
a
+
a
c
(iii)
2
p
2
q
2
−
3
p
q
+
4
,
5
+
7
p
q
−
3
p
2
q
2
2 p^{2} q^{2}-3 p q+4,5+7 p q-3 p^{2} q^{2}
2
p
2
q
2
−
3
pq
+
4
,
5
+
7
pq
−
3
p
2
q
2
(iv)
l
2
+
m
2
,
m
2
+
n
2
,
n
2
+
l
2
,
2
l
m
+
2
m
n
+
2
n
l
l^{2}+m^{2}, m^{2}+n^{2}, n^{2}+l^{2}, 2 l m+2 m n+2 n l
l
2
+
m
2
,
m
2
+
n
2
,
n
2
+
l
2
,
2
l
m
+
2
mn
+
2
n
l
Q2
EXERCISE 8.1
(a)
Subtract
4
a
−
7
a
b
+
3
b
+
12
4 a-7 a b+3 b+12
4
a
−
7
ab
+
3
b
+
12
from
12
a
−
9
a
b
+
5
b
−
3
12 a-9 a b+5 b-3
12
a
−
9
ab
+
5
b
−
3
(b)
Subtract
3
x
y
+
5
y
z
−
7
z
x
3 x y+5 y z-7 z x
3
x
y
+
5
yz
−
7
z
x
from
5
x
y
−
2
y
z
−
2
z
x
+
10
x
y
z
5 x y-2 y z-2 z x+10 x y z
5
x
y
−
2
yz
−
2
z
x
+
10
x
yz
(c)
Subtract
4
p
2
q
−
3
p
q
+
5
p
q
2
−
8
p
+
7
q
−
10
4 p^{2} q-3 p q+5 p q^{2}-8 p+7 q-10
4
p
2
q
−
3
pq
+
5
p
q
2
−
8
p
+
7
q
−
10
from
18
−
3
p
−
11
q
+
5
p
q
−
2
p
q
2
+
5
p
2
q
18-3 p-11 q+5 p q-2 p q^{2}+5 p^{2} q
18
−
3
p
−
11
q
+
5
pq
−
2
p
q
2
+
5
p
2
q
Q1
EXERCISE 8.2
Find the product of the following pairs of monomials.
(i)
4
,
7
p
4, 7p
4
,
7
p
(ii)
−
4
p
,
7
p
-4p, 7p
−
4
p
,
7
p
(iii)
−
4
p
,
7
p
q
-4p, 7pq
−
4
p
,
7
pq
(iv)
4
p
3
,
−
3
p
4p^3, -3p
4
p
3
,
−
3
p
(v)
4
p
,
0
4p, 0
4
p
,
0
Q2
EXERCISE 8.2
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
(
p
,
q
)
;
(
10
m
,
5
n
)
;
(
20
x
2
,
5
y
2
)
;
(
4
x
,
3
x
2
)
;
(
3
m
n
,
4
n
p
)
(p, q); (10m, 5n); (20x^2, 5y^2); (4x, 3x^2); (3mn, 4np)
(
p
,
q
)
;
(
10
m
,
5
n
)
;
(
20
x
2
,
5
y
2
)
;
(
4
x
,
3
x
2
)
;
(
3
mn
,
4
n
p
)
Q3
EXERCISE 8.2
Complete the table of products.
First monomial → Second monomial ↓
2
x
2x
2
x
−
5
y
-5y
−
5
y
3
x
2
3x^{2}
3
x
2
−
4
x
y
-4xy
−
4
x
y
7
x
2
y
7x^{2}y
7
x
2
y
−
9
x
2
y
2
-9x^{2}y^{2}
−
9
x
2
y
2
2
x
2x
2
x
4
x
2
4x^{2}
4
x
2
...
...
...
...
...
−
5
y
-5y
−
5
y
...
...
−
15
x
2
y
-15x^{2}y
−
15
x
2
y
...
...
...
3
x
2
3x^{2}
3
x
2
...
...
...
...
...
...
−
4
x
y
-4xy
−
4
x
y
...
...
...
...
...
...
7
x
2
y
7x^{2}y
7
x
2
y
...
...
...
...
...
...
−
9
x
2
y
2
-9x^{2}y^{2}
−
9
x
2
y
2
...
...
...
...
...
...
Q4
EXERCISE 8.2
Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
(i)
5
a
,
3
a
2
,
7
a
4
5a, 3a^2, 7a^4
5
a
,
3
a
2
,
7
a
4
(ii)
2
p
,
4
q
,
8
r
2p, 4q, 8r
2
p
,
4
q
,
8
r
(iii)
x
y
,
2
x
2
y
,
2
x
y
2
xy, 2x^2y, 2xy^2
x
y
,
2
x
2
y
,
2
x
y
2
(iv)
a
,
2
b
,
3
c
a, 2b, 3c
a
,
2
b
,
3
c
Q5
EXERCISE 8.2
Obtain the product of
(i)
x
y
,
y
z
,
z
x
xy, yz, zx
x
y
,
yz
,
z
x
(ii)
a
,
−
a
2
,
a
3
a, -a^2, a^3
a
,
−
a
2
,
a
3
(iii)
2
,
4
y
,
8
y
2
,
16
y
3
2, 4y, 8y^2, 16y^3
2
,
4
y
,
8
y
2
,
16
y
3
(iv)
a
,
2
b
,
3
c
,
6
a
b
c
a, 2b, 3c, 6abc
a
,
2
b
,
3
c
,
6
ab
c
(v)
m
,
−
m
n
,
m
n
p
m, -mn, mnp
m
,
−
mn
,
mn
p
Q1
EXERCISE 8.3
Carry out the multiplication of the expressions in each of the following pairs.
(i)
4
p
,
q
+
r
4p, q+r
4
p
,
q
+
r
(ii)
a
b
,
a
−
b
ab, a-b
ab
,
a
−
b
(iii)
a
+
b
,
7
a
2
b
2
a+b, 7a^2b^2
a
+
b
,
7
a
2
b
2
(iv)
a
2
−
9
,
4
a
a^2-9, 4a
a
2
−
9
,
4
a
(v)
p
q
+
q
r
+
r
p
,
0
pq+qr+rp, 0
pq
+
q
r
+
r
p
,
0
Q2
EXERCISE 8.3
Complete the table.
First expression
Second expression
Product
(i)
a
a
a
b
+
c
+
d
b+c+d
b
+
c
+
d
...
(ii)
x
+
y
−
5
x+y-5
x
+
y
−
5
5
x
y
5xy
5
x
y
...
(iii)
p
p
p
6
p
2
−
7
p
+
5
6p^2-7p+5
6
p
2
−
7
p
+
5
...
(iv)
4
p
2
q
2
4p^2q^2
4
p
2
q
2
p
2
−
q
2
p^2-q^2
p
2
−
q
2
...
(v)
a
+
b
+
c
a+b+c
a
+
b
+
c
a
b
c
abc
ab
c
...
Q3
EXERCISE 8.3
Find the product.
(i)
(
a
2
)
×
(
2
a
22
)
×
(
4
a
26
)
(a^2) \times (2a^{22}) \times (4a^{26})
(
a
2
)
×
(
2
a
22
)
×
(
4
a
26
)
(ii)
(
2
3
x
y
)
×
(
−
9
10
x
2
y
2
)
(\frac{2}{3}xy) \times (\frac{-9}{10}x^2y^2)
(
3
2
x
y
)
×
(
10
−
9
x
2
y
2
)
(iii)
(
−
10
3
p
q
3
)
×
(
6
5
p
3
q
)
(-\frac{10}{3}pq^3) \times (\frac{6}{5}p^3q)
(
−
3
10
p
q
3
)
×
(
5
6
p
3
q
)
(iv)
x
×
x
2
×
x
3
×
x
4
x \times x^2 \times x^3 \times x^4
x
×
x
2
×
x
3
×
x
4
Q4
EXERCISE 8.3
(a)
Simplify
3
x
(
4
x
−
5
)
+
3
3x(4x-5)+3
3
x
(
4
x
−
5
)
+
3
and find its values for (i)
x
=
3
x=3
x
=
3
(ii)
x
=
1
2
x=\frac{1}{2}
x
=
2
1
.
(b)
Simplify
a
(
a
2
+
a
+
1
)
+
5
a(a^2+a+1)+5
a
(
a
2
+
a
+
1
)
+
5
and find its value for (i)
a
=
0
a=0
a
=
0
, (ii)
a
=
1
a=1
a
=
1
(iii)
a
=
−
1
a=-1
a
=
−
1
.
Q5
EXERCISE 8.3
(a)
Add:
p
(
p
−
q
)
,
q
(
q
−
r
)
p(p-q), q(q-r)
p
(
p
−
q
)
,
q
(
q
−
r
)
and
r
(
r
−
p
)
r(r-p)
r
(
r
−
p
)
(b)
Add:
2
x
(
z
−
x
−
y
)
2x(z-x-y)
2
x
(
z
−
x
−
y
)
and
2
y
(
z
−
y
−
x
)
2y(z-y-x)
2
y
(
z
−
y
−
x
)
(c)
Subtract:
3
l
(
l
−
4
m
+
5
n
)
3l(l-4m+5n)
3
l
(
l
−
4
m
+
5
n
)
from
4
l
(
10
n
−
3
m
+
2
l
)
4l(10n-3m+2l)
4
l
(
10
n
−
3
m
+
2
l
)
(d)
Subtract:
3
a
(
a
+
b
+
c
)
−
2
b
(
a
−
b
+
c
)
3a(a+b+c)-2b(a-b+c)
3
a
(
a
+
b
+
c
)
−
2
b
(
a
−
b
+
c
)
from
4
c
(
−
a
+
b
+
c
)
4c(-a+b+c)
4
c
(
−
a
+
b
+
c
)
Q1
EXERCISE 8.4
Multiply the binomials.
(i)
(
2
x
+
5
)
(2x+5)
(
2
x
+
5
)
and
(
4
x
−
3
)
(4x-3)
(
4
x
−
3
)
(ii)
(
y
−
8
)
(y-8)
(
y
−
8
)
and
(
3
y
−
4
)
(3y-4)
(
3
y
−
4
)
(iii)
(
2.5
l
−
0.5
m
)
(2.5l-0.5m)
(
2.5
l
−
0.5
m
)
and
(
2.5
l
+
0.5
m
)
(2.5l+0.5m)
(
2.5
l
+
0.5
m
)
(iv)
(
a
+
3
b
)
(a+3b)
(
a
+
3
b
)
and
(
x
+
5
)
(x+5)
(
x
+
5
)
(v)
(
2
p
q
+
3
q
2
)
(2pq+3q^2)
(
2
pq
+
3
q
2
)
and
(
3
p
q
−
2
q
2
)
(3pq-2q^2)
(
3
pq
−
2
q
2
)
(vi)
(
3
4
a
2
+
3
b
2
)
(\frac{3}{4}a^2+3b^2)
(
4
3
a
2
+
3
b
2
)
and
4
(
a
2
−
2
3
b
2
)
4(a^2-\frac{2}{3}b^2)
4
(
a
2
−
3
2
b
2
)
Q2
EXERCISE 8.4
Find the product.
(i)
(
5
−
2
x
)
(
3
+
x
)
(5-2x)(3+x)
(
5
−
2
x
)
(
3
+
x
)
(ii)
(
x
+
7
y
)
(
7
x
−
y
)
(x+7y)(7x-y)
(
x
+
7
y
)
(
7
x
−
y
)
(iii)
(
a
2
+
b
)
(
a
+
b
2
)
(a^2+b)(a+b^2)
(
a
2
+
b
)
(
a
+
b
2
)
(iv)
(
p
2
−
q
2
)
(
2
p
+
q
)
(p^2-q^2)(2p+q)
(
p
2
−
q
2
)
(
2
p
+
q
)
Q3
EXERCISE 8.4
Simplify.
(i)
(
x
2
−
5
)
(
x
+
5
)
+
25
(x^2-5)(x+5)+25
(
x
2
−
5
)
(
x
+
5
)
+
25
(ii)
(
a
2
+
5
)
(
b
3
+
3
)
+
5
(a^2+5)(b^3+3)+5
(
a
2
+
5
)
(
b
3
+
3
)
+
5
(iii)
(
t
+
s
2
)
(
t
2
−
s
)
(t+s^2)(t^2-s)
(
t
+
s
2
)
(
t
2
−
s
)
(iv)
(
a
+
b
)
(
c
−
d
)
+
(
a
−
b
)
(
c
+
d
)
+
2
(
a
c
+
b
d
)
(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)
(
a
+
b
)
(
c
−
d
)
+
(
a
−
b
)
(
c
+
d
)
+
2
(
a
c
+
b
d
)
(v)
(
x
+
y
)
(
2
x
+
y
)
+
(
x
+
2
y
)
(
x
−
y
)
(x+y)(2x+y)+(x+2y)(x-y)
(
x
+
y
)
(
2
x
+
y
)
+
(
x
+
2
y
)
(
x
−
y
)
(vi)
(
x
+
y
)
(
x
2
−
x
y
+
y
2
)
(x+y)(x^2-xy+y^2)
(
x
+
y
)
(
x
2
−
x
y
+
y
2
)
(vii)
(
1.5
x
−
4
y
)
(
1.5
x
+
4
y
+
3
)
−
4.5
x
+
12
y
(1.5x-4y)(1.5x+4y+3)-4.5x+12y
(
1.5
x
−
4
y
)
(
1.5
x
+
4
y
+
3
)
−
4.5
x
+
12
y
(viii)
(
a
+
b
+
c
)
(
a
+
b
−
c
)
(a+b+c)(a+b-c)
(
a
+
b
+
c
)
(
a
+
b
−
c
)
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