Question

Of which of the binomials given below is m²n² + 14mnpq + 49p²q² the expansion?

Options

• (m  + n) (p + q)

• (mn − pq)

• (7mn + pq)

• (mn + 7pq)

Answer 1

(mn + 7pq)

Explanation:

Let us check each of the given options.

(m + n)(p + q)

= m(p + q) + n(p + q)

= mp + mq + np + nq

So, it is not the correct option.

(mn − pq)²

= (mn)² − 2 × (mn) × (pq) + (pq)²  ...[∵ (a − b)² = a² − 2ab + b²]

= m²n² − 2mnpq + p²q²

So, it is not the correct option.

(7mn + pq)²

= (7mn)² + 2 × (7mn) × (pq) + (pq)² ......[∵ (a + b)² = a² + 2ab + b²]

= 49m²n² + 14mnpq + p²q²

So, it is not a correct option.

(mn + 7pq)²

= (mn)² + 2 × (mn) × (7pq) + (7pq)² ...[∵ (a + b)² = a² + 2ab + b²]

= m²n² + 14mnpq + 49p²q²

So, it is a correct option.

Hence, the correct answer is option (mn + 7pq)².