# Algebraic expressions NCERT Questions

NCERT TEXT BOOK EXERCISES

EXERCISE-9.1

1. 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

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

(i)    ab − bcbc − caca − ab

(ii)   a − b + abb − c + bcc − a + ac

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

(iv) l2 + m2m2 + n2n2 + l2, 2lm +2mn + 2nl

1. (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

1. Find the product of the following pairs of monomials.

(i) 4, 7p                                                       (ii) − 4p, 7p

(iii) − 4p, 7pq                                              (iv) 4p3, − 3p (v) 4p, 0

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

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

1. Complete the table of products.
 2x − 5y 3x2 − 4xy 7x2y − 9x2y2 2x 4x2 … … … … … − 5y … … − 15x2y … … … 3x2 … … … … … … − 4xy … … … … … … 7x2y … … … … … … − 9x2y2 … … … … … …
1. 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

1. Obtain the product of

(i) xy, yzzx (ii) a, − a2a3 (iii) 2, 4y, 8y2, 16y3 (iv) a, 2b, 3c, 6abc (v) m, − mnmnp

EXERCISE-9.3

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

(i) 4pq + r                                                 (ii) aba − b

(iii) a + b, 7a2b2                                                                (iv) a2 − 9, 4a

(v) pq + qr + rp, 0

1. 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 –

1. Find the product.

(i)    (a2) × (2a22) × (4a26)                             (ii)

(iii)                              (iv)   x × x2 × x3 × x4

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

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

1. (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

1. 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) and

1. Find the product.

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

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

1. 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

1. 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)

1. Use the identity (xa) (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) (4− 1)                                    (iv) (4x + 5) (4− 1)

(v) (2x +5y) (2x + 3y)                                   (vi) (2a2 +9) (2a2 + 5)

(vii) (xyz − 4) (xyz − 2)

1. 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

1. 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

1. Show that

(i)    (3x + 7)2 − 84x = (3x − 7)2

(ii)   (9p − 5q)2 + 180pq = (9p + 5q)2

(iii)

(iv) (4pq + 3q)− (4pq − 3q)2 = 48pq2

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

1. Using identities, evaluate.

(i) 712                                                                                       (ii) 992

(iii) 1022                                                     (iv) 9982

(v) (5.2)2                                                     (vi) 297 × 303

(vii) 78 × 82                                                (viii) 8.92 (ix) 1.05 × 9.5

1. Using a− b2= (a + b) (a − b), find

(i) 512 − 492 (ii) (1.02)2 − (0.98)2 (iii) 1532 − 1472(iv) 12.12 − 7.92

1. Using (a) (b) = x2+ (a + bx + ab, find

(i) 103 × 104                                              (ii) 5.1 × 5.2

(iii) 103 × 98                                               (iv) 9.7 × 9.8

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