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Byju's Answer
Standard IX
Mathematics
(x±a)(x±b) = x²±(a+b)x+ab.
Of which of t...
Question
Of which of the binomials given below is m
2
n
2
+ 14mnpq + 49p
2
q
2
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
= a
2
− 2ab + b
2
]
= m
2
n
2
− 2mnpq + p
2
q
2
So, it is not a correct option.
(iii) (7mn + pq)
2
= (7mn)
2
+ 2 × (7mn) × (pq) + (pq)
2
[∵ (a + b)
2
= a
2
+ 2ab + b
2
]
= 49m
2
n
2
+ 14mnpq + p
2
q
2
So, it is not a correct option.
(iv) (mn + 7pq)
2
= (mn)
2
+ 2 × (mn) × (7pq) + (7pq)
2
[∵ (a + b)
2
= a
2
+ 2ab + b
2
]
= m
2
n
2
+ 14mnpq + 49p
2
q
2
So, it is a correct option.
Hence, the correct answer is option (iv).
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