# NCERT Solutions for Class 8 Maths Maths - NCERT Solution Chapter 9

## Algebraic Expressions and Identities Class 8

### Exercise 9.1 : Solutions of Questions on Page Number : 140

Q1 :

Identify the terms, their coefficients for each of the following expressions.

(i) 5xyz2 - 3zy

(ii) 1 + x + x2

(iii) 4x2y2 - 4x2y2z2 + z2

(iv) 3 - pq + qr - rp

(v)

(vi) 0.3a - 0.6ab + 0.5b

The terms and the respective coefficients of the given expressions are as follows.

 - Terms Coefficients (i) 5xyz2 - 3zy 5 - 3 (ii) 1 x x2 1 1 1 (iii) 4x2y2 - 4x2y2z2 z2 4 - 4 1 (iv) 3 - pq qr - rp 3 - 1 1 - 1 (v) - xy - 1 (vi) 0.3a - 0.6ab 0.5b 0.3 - 0.6 0.5

Q2 :

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

x + y, 1000, x + x2 + x3 + x4, 7 + y + 5x, 2y - 3y2, 2y - 3y2 + 4y3, 5x - 4y + 3xy, 4z - 15z2, ab + bc + cd + da, pqr, p2q + pq2, 2p + 2q

The given expressions are classified as

Monomials: 1000, pqr

Binomials: x + y, 2y - 3y2, 4z - 15z2, p2q + pq2, 2p + 2q

Trinomials: 7 + y + 5x, 2y - 3y2 + 4y3, 5x - 4y + 3xy

Polynomials that do not fit in any of these categories are

x+ x2+ x3+ x4, ab + bc + cd + da

Q3 :

(i) ab - bc, bc - ca, ca - ab

(ii) a - b + ab, b - c + bc, c - a + ac

(iii) 2p2q2 - 3pq + 4, 5 + 7pq - 3p2q2

(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl

Q4 :

(a) Subtract 4a - 7ab + 3b + 12 from 12a - 9ab + 5b - 3

(b) Subtract 3xy + 5yz - 7zx from 5xy - 2yz - 2zx + 10xyz

(c) Subtract 4p2q - 3pq + 5pq2 - 8p + 7q - 10 from 18 - 3p - 11q + 5pq - 2pq2 + 5p2q

### Exercise 9.2 : Solutions of Questions on Page Number : 143

Q1 :

Find the product of the following pairs of monomials.

(i) 4, 7p (ii) - 4p, 7p (iii) - 4p, 7pq

(iv) 4p3, - 3p (v) 4p, 0

Q2 :

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.

(p, q); (10m, 5n); (20x2, 5y2); (4x, 3x2); (3mn, 4np)

Q3 :

Complete the table of products.

 2x - 5y 3x2 - 4xy 7x2y - 9x2y2 2x 4x2 … … … … … - 5y … … - 15x2y … … … 3x2 … … … … … … - 4

Q4 :

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

(i) 5a, 3a2, 7a4 (ii) 2p, 4q, 8r (iii) xy, 2x2y, 2xy2

(iv) a, 2b, 3c

Q5 :

Obtain the product of

(i) xy, yz, zx (ii) a, - a2, a3 (iii) 2, 4y, 8y2, 16y3

(iv) a, 2b, 3c, 6abc (v) m, - mn, mnp

### Exercise 9.3 : Solutions of Questions on Page Number : 146

Q1 :

Carry out the multiplication of the expressions in each of the following pairs.

(i) 4p, q + r (ii) ab, a - b (iii) a + b, 7a2b2

(iv) a2 - 9, 4a (v) pq + qr + rp, 0

Q2 :

Complete the table

 --- First expression Second Expression Product (i) a b + c + d - (ii) x + y - 5 5 xy - (iii) p 6p2 - 7p + 5 - (iv) 4p2q2 p2 - q2 - (v) a + b + c abc -

Q3 :

Find the product.

(i) (a2) × (2a22) × (4a26)

(ii)

(iii)

(iv) x × x2 × x3 × x4

Q4 :

(a) Simplify 3x (4x - 5) + 3 and find its values for (i) x = 3, (ii) .

(b) a (a2 + a + 1) + 5 and find its values for (i) a = 0, (ii) a = 1, (iii) a = - 1.

Q5 :

(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)

### Exercise 9.4 : Solutions of Questions on Page Number : 148

Q1 :

Multiply the binomials.

(i) (2x + 5) and (4x - 3) (ii) (y - 8) and (3y - 4)

(iii) (2.5l - 0.5m) and (2.5l + 0.5m) (iv) (a + 3b) and (x + 5)

(v) (2pq + 3q2) and (3pq - 2q2)

(vi)

Q2 :

Find the product.

(i) (5 - 2x) (3 + x) (ii) (x + 7y) (7x - y)

(iii) (a2 + b) (a + b2) (iv) (p2 - q2) (2p + q)

Q3 :

Simplify.

(i) (x2 - 5) (x + 5) + 25

(ii) (a2 + 5) (b3 + 3) + 5

(iii) (t + s2) (t2 - s)

(iv) (a + b) (c - d) + (a - b) (c + d) + 2 (ac + bd)

(v) (x + y) (2x + y) + (x + 2y) (x - y)

(vi) (x + y) (x2 - xy + y2)

(vii) (1.5x - 4y) (1.5x + 4y + 3) - 4.5x + 12y

(viii) (a + b + c) (a + b - c)

### Exercise 9.5 : Solutions of Questions on Page Number : 151

Q1 :

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

(i) (x + 3) (x + 3) (ii) (2y + 5) (2y + 5)

(iii) (2a - 7) (2a - 7) (iv)

(v) (1.1m - 0.4) (1.1 m + 0.4) (vi) (a2 + b2) ( - a2 + b2)

(vii) (6x - 7) (6x + 7) (viii) ( - a + c) ( - a + c)

(ix) (x) (7a - 9b) (7a - 9b)

Q2 :

Use the identity (x + a) (x + b) = x2 + (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) (2a2 +9) (2a2 + 5)

(vii) (xyz - 4) (xyz - 2)

Q3 :

Find the following squares by suing the identities.

(i) (b - 7)2 (ii) (xy + 3z)2 (iii) (6x2 - 5y)2

(iv) (v) (0.4p - 0.5q)2 (vi) (2xy + 5y)2

Q4 :

Simplify.

(i) (a2 - b2)2 (ii) (2x +5)2 - (2x - 5)2

(iii) (7m - 8n)2 + (7m + 8n)2 (iv) (4m + 5n)2 + (5m + 4n)2

(v) (2.5p - 1.5q)2 - (1.5p - 2.5q)2

(vi) (ab + bc)2 - 2ab2c (vii) (m2 - n2m)2 + 2m3n2

Q5 :

Show that

(i) (3x + 7)2 - 84x = (3x - 7)2 (ii) (9p - 5q)2 + 180pq = (9p + 5q)2

(iii)

(iv) (4pq + 3q)2 - (4pq - 3q)2 = 48pq2

(v) (a - b) (a + b) + (b - c) (b + c) + (c - a) (c + a) = 0

Q6 :

Using identities, evaluate.

(i) 712 (ii) 992 (iii) 1022 (iv) 9982

(v) (5.2)2 (vi) 297 x 303 (vii) 78 x 82

(viii) 8.92 (ix) 1.05 x 9.5

Q7 :

Using a2 - b2 = (a + b) (a - b), find

(i) 512 - 492 (ii) (1.02)2 - (0.98)2 (iii) 1532 - 1472

(iv) 12.12 - 7.92

Q8 :

Using (x + a) (x + b) = x2 + (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