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Question
Show that `(4pq + 3q)^2 - (4pq - 3q)^2 = 48pq^2`
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Solution
L.H.S = (4pq + 3q)2 - (4pq - 3q)2
= (4pq)2 + 2(4pq)(3q) + (3q)2 = [(4pq)2 - 2(4pq)(3q) +(3q)2]
= 16p2q2 + 24pq2 + 9q2 - [16p2q2 - 24pq2 + 9q2]
= 16p2q2 + 24pq2 + 9q2 - 16p2q2 +24pq2 - 9q2
= 48pq2 = R.H.S
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