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Question
Of which of the binomials given below is m2n2 + 14mnpq + 49p2q2 the expansion?
(i) (m + n) (p + q) (ii) (mn- pq) (iii) (7mn + pq) (iv) (mn + 7pq)
Of which of the binomials given below is m2n2 + 14mnpq + 49p2q2 the expansion?
(i) (m + n) (p + q) (ii) (mn- pq) (iii) (7mn + pq) (iv) (mn + 7pq)
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Solution
Let us check each of the given options.
(i) (m + n)(p + q)
= m(p + q) + n(p + q)
= mp + mq + np + nq
So, it is not a correct option.
(ii) (mn − pq)2
= (mn)2 − 2 × (mn) × (pq) + (pq)2 [∵ (a − b)2 = a2 − 2ab + b2]
= m2n2 − 2mnpq + p2q2
So, it is not a correct option.
(iii) (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.
(iv) (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 (iv).
Let us check each of the given options.
(i) (m + n)(p + q)
= m(p + q) + n(p + q)
= mp + mq + np + nq
So, it is not a correct option.
(ii) (mn − pq)2
= (mn)2 − 2 × (mn) × (pq) + (pq)2 [∵ (a − b)2 = a2 − 2ab + b2]
= m2n2 − 2mnpq + p2q2
So, it is not a correct option.
(iii) (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.
(iv) (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 (iv).
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