NCERT TEXT BOOK EXERCISES
EXERCISE-9.1
- 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
- Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
- Add the following.
(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
- (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
- Find the product of the following pairs of monomials.
(i) 4, 7p (ii) − 4p, 7p
(iii) − 4p, 7pq (iv) 4p3, − 3p (v) 4p, 0
- 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)
- Complete the table of products.
| 2x | − 5y | 3x2 | − 4xy | 7x2y | − 9x2y2 | |
| 2x | 4x2 | … | … | … | … | … |
| − 5y | … | … | − 15x2y | … | … | … |
| 3x2 | … | … | … | … | … | … |
| − 4xy | … | … | … | … | … | … |
| 7x2y | … | … | … | … | … | … |
| − 9x2y2 | … | … | … | … | … | … |
- 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
- 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
- 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
- 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 | – |
- Find the product.
(i) (a2) × (2a22) × (4a26) (ii)
(iii) (iv) x × x2 × x3 × x4
- (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.
- (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
- 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
- Find the product.
(i) (5 − 2x) (3 + x) (ii) (x + 7y) (7x − y)
(iii) (a2 + b) (a + b2) (iv) (p2 − q2) (2p + q)
- 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
- 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)
- 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)
- 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
- 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
- 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
- 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
- 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
- Using (x + a) (x + b) = x2+ (a + b) x + ab, find
(i) 103 × 104 (ii) 5.1 × 5.2
(iii) 103 × 98 (iv) 9.7 × 9.8