Question

Find the product:-
i. (pq + 5) (pq + 3)​

Answer 1

$\large\bold{\underline{\underline{Answer:-}}}$

$\large{\underline{\boxed{\sf pq^2+ 8pq + 15}}}$

$\large\bold{\underline{\underline{Explanation:-}}}$

Given that ;

$\tt \implies (pq + 5)(pq + 3)$

It can be solved using two methods.

Method I : By multiplying the terms.

$\tt \implies (pq + 5)(pq + 3) \\ \\ \tt \implies pq(pq + 5) + 3(pq + 5) \\ \\ \tt \implies (pq) {}^{2} + 5pq + 3pq + 15 \\ \\ \tt \implies pq {}^{2} + 8pq + 15$

Hence, the answer is (p² + 8pq + 15).

$\rule{300}{2}$

Method II: By using identity :-

(x + a)(x + b) = x² + (a + b)x + ab

Here x = pq, a = 5 and b = 3. On Substituting the values.

$\tt \implies (pq + 5)(pq + 3) \\ \\ \tt \implies (pq)^{2} + (5+ 3)pq + 5 \times 3 \\ \\ \tt \implies pq^{2} + 8pq + 15$

Hence, the answer is (pq² + 8pq + 15).

Answer 2

(pq+5) (pq+3)

pq(pq+3) + 5(pq+3)

pq^2+3pq+5pq+15

pq^2+8pq+15

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