Exercise 8.3
1. Carry out the multiplication of the expressions in each of the following pairs.
(i) 4p, q + r : 4p(q + r) =
(ii) ab, a – b : ab(a – b) =
(iii) a + b, 7 a 2 b 2 a + b 7 a 2 b 2
(iv) a 2 − 9 , 4a : a 2 − 9 4 a
(v) pq + qr + rp, 0 : (pq + qr + rp) × 0 =
2. Complete the table.
| S.No. | First expression | Second expression | Product |
|---|---|---|---|
| (i) | a | b+c+d | |
| (ii) | x + y – 5 | 5xy | |
| (iii) | p | ||
| (iv) | |||
| (v) | a+b+c | abc |
3. Find the product.
(i) a 2 × 2 a 22 × 4 a 26 2 × 4 a 2 × a 22 × a 26 8 × a 2 + 22 + 26
(ii) 2 3 xy × − 9 10 x 2 y 2 2 3 × − 9 10 x × x 2 × y × y 2
(iii) − 10 3 pq 3 6 5 p 3 q = (− 10 3 × 6 5 p × p 3 × q 3 × q ) =
(iv) x × x 2 × x 3 × x 4 x 1 + 2 + 3 + 4
4. (a) Simplify 3x (4x – 5) + 3 and find its values for (i) x = 3 (ii) x =
(i) Putting x = 3 in the equation: 12 x 2 − 15 x + 3 = 12 3 2 − 15 3 + 3 =
(ii) Putting x =1 2 12 x 2 − 15 x + 3 = 12 1 2 2 − 15 1 2 + 3 = 12 x
= 15 2
(b) Simplify
(i) putting a = 0 in the equation: 0 3 + 0 2 + 0 + 5 =
(ii) putting a = 1 in the equation: 1 3 + 1 2 + 1 + 5 =
(iii) Putting a = -1 in the equation: − 1 3 + − 1 2 + − 1 + 5 =
5. (a) Add: p (p – q), q (q – r) and r (r – p)
p(p – q) + q(q – r) + r(r – p) = q 2
=
(b) Add: 2x (z – x – y) and 2y (z – y – x)
2x(z – x – y) + 2y(z – y – x) = x 2 y 2
= x 2 y 2
(c) Subtract: 3l(l – 4m + 5n) from 4l(10n – 3m + 2l)
= 40 ln − 12 lm + 8 l 2 − 3 l 2 + 12 lm − 15 ln = l 2
(d) Subtract: 3a(a + b + c) – 2b(a – b + c) from 4c(–a + b + c)
4c(–a+b+c) – (3a(a+b+c) – 2b(a–b+c)) = − 4 ac + 4 bc + 4 c 2 3 a 2 + 3 ab + 3 ac − 2 ab − 2 b 2 + 2 bc
= c 2 a 2 b 2
= − 4 ac + 4 bc + 4 c 2 a 2 b 2
= c 2 a 2 b 2