Question

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

Answer 1

(i) 4p(q + r) 
= 4pq + 4pr

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(ii) ab(a – b) 
= a² b – a b²

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(iii) (a + b) (7a²b²) 
= 7a³b² + 7a²b³

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(iv) (a² – 9)(4a) 
= 4a³ – 36a

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(v) (pq + qr + rp) × 0 = 0 

Answer 2

Let's carry out the multiplication for each of the given pairs of expressions:

(i) 4p and q+r
\(4p \cdot (q + r) = 4p \cdot q + 4p \cdot r\)
\(= 4pq + 4pr\)
So, the result is: \(4pq + 4pr\)

(ii) ab and a - b
\(ab \cdot (a - b) = ab \cdot a - ab \cdot b\)
\(= a^2b - ab^2\)
So, the result is: \(a^2b - ab^2\)

(iii) a+b and \(7a^2b^2\)
\((a + b) \cdot 7a^2b^2 = a \cdot 7a^2b^2 + b \cdot 7a^2b^2\)
\(= 7a^3b^2 + 7a^2b^3\)
So, the result is: \(7a^3b^2 + 7a^2b^3\)

(iv) \(a^2 - 9\) and 4a
\((a^2 - 9) \cdot 4a = a^2 \cdot 4a - 9 \cdot 4a\)
\(= 4a^3 - 36a\)
So, the result is: \(4a^3 - 36a\)

(v) pq+qr+rp and 0
\((pq + qr + rp) \cdot 0 = 0\)
So, the result is: 0