Chapter 9: Algebraic Expressions and Identities
Ex 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) + – xy
(vi) 0.3a – 0.6ab + 0.5b
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
(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
4. (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
Chapter 9 Ex 9.1 Algebraic Expressions and identities free pdf
Ex 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
2. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
(p, q); (10m, 5n); (20×2, 5y2); (4x, 3×2); (3mn, 4np)
3. Complete the table of Products.
| 1st Monomial | 2x | -5y | 3x2 | -4xy | 7x2y | -9x2y2 |
| 2nd Monomial | ||||||
| 2x | ||||||
| -5y | ||||||
| 3x2 | ||||||
| -4xy | ||||||
| 7x2y | ||||||
| -9x2y2 |
4.Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
(ii) 2p, 4q, 8r (iii) xy, 2x2y, 2xy2
(i) xy, yz, zx (ii) a, -a2, a3 (iii) 2, 4y, 8y2, 16y3 (iv) a, 2b, 3c, 6abc (v) m, -mn, mnp
Chapter 9 Ex 9.2 Algebraic Expressions and identities free pdf
Ex 9.3
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, 7a2b2 (iv) a2 – 9, 4a (v) pq + qr + rp, 0
| First Expression | Second Expression | Product |
| a | b + c + d | |
| x + y – 5 | 5xy | |
| p | 6p2 – 7p + 5 | |
| 4p2q2 | P2 – q2 | |
| a + b + c | abc |
i. a2 × 2a22 × 4a26
ii. (2/3 xy) × (-9/10 x2 y2)
iii. (-10/3 pq3) × (6/5 p3q)
iv. X × x2 × x3 × x4
4. Simplify
(a) 3x (4x-5) + 3 and find its values for (i) x= 3 (ii) x= 1/2
(b) Simplify: a (a2 + a + 1) + 5 and find its value for (i) a = 0 (ii) a = 1 (iii) a = -1
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)
Chapter 9 Algebraic expression and identities ex 9.3 free pdf
Ex 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) (a2 + 3b2) and 4(a2 – b2)
(ii) (x + 7y) (7x – y)
(iii) (a2 + b) (a + b2)
(iv) (p2 – q2)(2p + q)
3. 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)
Chapter 9 Algebraic expression and identities ex 9.4 free pdf
Ex 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) (3a – ) (3a – )
(v) (1.1m – 0.4) (1.1m + 0.4)
(vi) (a2 + b2) (-a2 + b2)
(vii) (6x – 7) (6x + 7)
(viii) (-a + c) (-a + c)
(ix) ( + ) ( + )
(x) (7a – 9b) (7a – 9b)
2. 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)
3. Find the following squares by using the identities.
(i) (b – 7)2
(ii) (xy + 3z)2
(iii) (6×2 – 5y)2
(iv) ( m + n)2
(v) (0.4p – 0.5q)2
(vi) (2xy + 5y)2
(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
(i) (3x + 7)2 – 84x = (3x – 7)2
(ii) (9p – 5q)2 + 180pq = (9p + 5q)2
(iii) ( m – n)2 + 2mn = m2 + n2
(iv) (4pq + 3q)2 – (4pq – 3q)2 = 48pq2
(v) (a – b)(a + b) + (b – c) (b + c) + (c – a) (c + a) = 0
6. Use identities, evaluate
(i) 712
(ii) 992
(iii) 1022
(iv) 9982
(v) 5.22
(vi) 297 × 303
(vii) 78 × 82
(viii) 8.92
(ix) 1.05 × 9.5
7. Using a2 – b2 = (a + b) (a – b), find
(i) (51)2 – (49)2
(ii) (1.02)2 – (0.98)2
(iii) (153)2 – (147)2
(iv) (12.1)2 – (7.9)2
8. 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
Chapter 9 ex 9.5 algebraic expressions and identities free pdf
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