NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities, are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities.

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.1

Question 1.
Identify the terms, their coefficients for each of the following expressions:
(i) \({ 5xyz }^{ 2 }-3zy\)
(ii) \(1+x+{ x }^{ 2 }\)
(iii) \(4{ x }^{ 2 }{ y }^{ 2 }-4{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }+{ z }^{ 2 }\)
(iv) 3 – pq + qr – rp
(v) \(\frac { x }{ 2 } +\frac { y }{ 2 } -xy\)
(vi) 0.3a – 0.6ab + 0.5b.
Solution.
(i) \({ 5xyz }^{ 2 }-3zy\)

(ii) \(1+x+{ x }^{ 2 }\)

(iii) \(4{ x }^{ 2 }{ y }^{ 2 }-4{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }+{ z }^{ 2 }\)

(iv) 3 – pq + qr – rp

(v) \(\frac { x }{ 2 } +\frac { y }{ 2 } -xy\)

(vi)0.3a – 0.6ab + 0.5b.

Question 2.
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

Solution.

Question 3.
Add the following.
(i) ab – be, be – ca, ca – ab
(ii) a -b + ab, b – c + be, c – a + ac
(iii) \(2{ p }^{ 2 }{ q }^{ 2 }-3pq+4,\quad 5+7pq-3{ p }^{ 2 }{ q }^{ 2 }\)
(iv) \({ l }^{ 2 }+{ m }^{ 2 },\quad { m }^{ 2 }+{ n }^{ 2 },\quad { n }^{ 2 }+{ l }^{ 2 }\), 2lm + 2mn + 2nl.
Solution.
(i) ab – be, be – ca, ca – ab

(ii) a -b + ab, b – c + be, c – a + ac

(iii) \(2{ p }^{ 2 }{ q }^{ 2 }-3pq+4,\quad 5+7pq-3{ p }^{ 2 }{ q }^{ 2 }\)

(iv) \({ l }^{ 2 }+{ m }^{ 2 },\quad { m }^{ 2 }+{ n }^{ 2 },\quad { n }^{ 2 }+{ l }^{ 2 }\), 2lm + 2mn + 2nl.

Question 4.
(a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 56 – 3
(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz
(c) Subtract \(4{ p }^{ 2 }q-3pq+5p{ q }^{ 2 }-8p+7q-10\) from \(18-3p-11q+5pq-2p{ q }^{ 2 }+5{ p }^{ 2 }q\)
Solution.

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.2

Question 1.
Find the product of the following pairs of monomials:
(i) 4, 7p
(ii) – 4p, 7p
(iii) – 4p, 7pq
(iv) \(4{ p }^{ 3, },\quad -3p\)
(v) 4p, 0.
Solution.

Question 2.
Find the areas of rectangles with the following pairs of mononials as their lengths and breadths respectively:
(i) (p, q);
(ii) (10m, 5n);
(iii) (\(20{ x }^{ 2 },\quad 5{ y }^{ 2 }\));
(iv) (\(4x,\quad 3{ x }^{ 2 }\));
(v) (3mn, 4np).
Solution.
(i) (p, q)
Length = p
Breadth = q
∴ Area of the rectangle
= Length x Breadth
= pxq
= pq

(ii) (10m, 5n)
Length = 10 m
Breadth = 5 n
∴ Area of the rectangle
= Length x Breadth
= (10m) x (5n)
= (10 x 5) x (m x n)
= 50 x (mn)
= 50 mn

(iii) (\(20{ x }^{ 2 },\quad 5{ y }^{ 2 }\))
Length = \(20{ x }^{ 2 }\)
Breadth = \(5{ y }^{ 2 }\)
∴ Area of the rectangle
= Length x Breadth
= (\(20{ x }^{ 2 }\)) x (\(5{ y }^{ 2 }\))
= (20 x 5) x (\({ x }^{ 2 }\times { y }^{ 2 }\))
= 100 x (\({ x }^{ 2 }{ y }^{ 2 }\))
= 100\({ x }^{ 2 }{ y }^{ 2 }\)

(iv) (4x, 3xP)
Length = 4.x
Breadth = \(3{ x }^{ 2 }\)
∴ Area of the rectangle
= Length x Breadth =
(4x) x (\(3{ x }^{ 2 }\))
= (4 x 3) x (\(x\times { x }^{ 2 }\))
= 12 x \({ x }^{ 3 }\)
= 12×3

(v) (3mn, 4np)
Length = 3 mn
Breadth = 4np
∴ Area of the rectangle
= Length x Breadth
= (3mn) x (4np)
= (3 x 4) x (mn) x (np)
= 12 x m x (n x n) x p
= 12\(m{ n }^{ 2 }p\)

Question 3.
Complete the table of products.

Solution.

Question 4.
Obtain the volume of rectangular boxes with the following length, breadth and height respectively:
(i) \(5a,\quad 3{ a }^{ 2 },\quad 7{ a }^{ 4 }\)
(ii) 2p, 4q, 8r
(iii) \(xy,\quad 2{ x }^{ 2 }y,\quad 2x{ y }^{ 2 }\)
(iv) a, 2b, 3c
Solution.
(i) \(5a,\quad 3{ a }^{ 2 },\quad 7{ a }^{ 4 }\)

(ii) 2p, 4q, 8r

(iii) \(xy,\quad 2{ x }^{ 2 }y,\quad 2x{ y }^{ 2 }\)

(iv) a, 2b, 3c

Question 5.
Obtain the product of
(i) xy, yz, zx
(ii) \(a,\quad -{ a }^{ 2 },\quad { a }^{ 3 }\)
(iii) \(2,\quad 4y,\quad 8{ y }^{ 2 },\quad 16{ y }^{ 3 }\)
(iv) a, 2b, 3c, 6abc
(v) m, – mn, mnp.
Solution.
(i) xy, yz, zx
Required product
= (xy) x (yz) x (zx)

(ii) \(a,\quad -{ a }^{ 2 },\quad { a }^{ 3 }\)

(iii) \(2,\quad 4y,\quad 8{ y }^{ 2 },\quad 16{ y }^{ 3 }\)

(iv) a, 2b, 3c, 6abc

(v) m, – mn, mnp.

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.3

Question 1.
Carry out the multiplication of the expressions in each of the following pairs:
(i) 4p, q + r
(ii) ab, a – b
(iii) \(a+b,\quad 7{ a }^{ 2 }{ b }^{ 2 }\)
(iv) \({ a }^{ 2 }-9,\quad 4a\)
(v) pq + qr + rp, 0
Solution.

Question 2.
Complete the table

Solution.

Question 3.
Find the product:


Solution.

Question 4.
(a) Simplify: 3x (4x – 5) + 3 and find its values for (i) x = 3, (ii) \(x=\frac { 1 }{ 2 } \)
(b) Simplify: \(a({ a }^{ 2 }+a+1)+5\) and find its value for (i)a = 0, (ii)a = 1 and (iii) a = -1.
Solution.

Question 5.
(a) Add: p(p – q), q(q – r) and r(r -p)
(b) Add: 2x(z – x – y) and 2y (z – y – x)
(c) Subtract: 3l (l – 4m + 5n) from 4l (10n – 3m + 2l)
(d) Subtract: 3a(a + b + c) – 2b(a – b + c) from 4c(- a + b + c).
Solution.

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.4

Question 1.
Multiply the binomials:
(i) (2x + 5) and (4x – 3)
(ii) (y – 8) and (3y – 4)
(iii) (2.5l – 0.5 m) and (2.5l + 0.5m)
(iv) (a + 3b) and (x + 5)
(v) \((2pq+3{ q }^{ 2 })\quad and\quad (3pq-2{ q }^{ 2 })\)
(vi) \((\frac { 3 }{ 4 } { a }^{ 2 }+3{ b }^{ 2 })\quad and\quad 4({ a }^{ 2 }-\frac { 2 }{ 3 } { b }^{ 2 })\)
Solution.

Question 2.
Find the product:
(i) (5 – 2x) (3 + x)
(ii) (x + 7y) (7x —y)
(iii) \(({ a }^{ 2 }+b)(a+{ b }^{ 2 })\)
(iv) \(({ p }^{ 2 }-{ q }^{ 2 })(2p+q)\)
Solution.

Question 3.
Simplify.

Solution.

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.5

Question 1.
Use a suitable identity to get each of the following products:


Solution.

Question 2.
Use the identity \((x+a)(x+b)={ x }^{ 2 }+(a+b)x+ab\) to find the following products:
(i) (x + 3) (x + 7)
(ii) (4x + 5) (4x + 1)
(iii) (4x – 5) (4x – 1)
(iv) (4x + 5) (4x – 1)
(v) (2x + 5y) (2x + 3y)
(vi) \((2{ a }^{ 2 }+9)(2{ a }^{ 2 }+5)\)
(vii) (xyz – 4) (xyz – 2).
Solution.

Question 3.
Find the following squares by using the identities.

Solution.

Question 4.
Simplify:

Solution.

Question 5.
Show that:

Solution.

Question 6.
Using identities, evaluate:

Solution.

Question 7.
Using \({ a }^{ 2 }-{ b }^{ 2 }=(a+b)(a-b)\), find

Solution.

Question 8.
Using \((x+a)(x+b)={ x }^{ 2 }+(a+b)x+ab\), find
(i) 103 x 104
(ii) 5.1 x 5.2
(iii) 103 x 98
(iv) 9.7 x 9.8
Solution.

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