Question

Prove that :(7x +8y)2 – (7x – 8y)2 = 224xy

Answer 1

Answer:

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Answer 2

${(7x + 8y)}^{2} - {(7x - 8y)}^{2} = 224xy \\ lhs = {(7x + 8y)}^{2} - {(7x - 8y)}^{2} \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ [(7x + 8y) + (7x - 8y)][(7x + 8y) - (7x - 8y)] \\ = [7x + 8y + 7x - 8y][7x + 8y - 7x + 8y] \\ = (14x)(16y) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 224xy = rhs \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ hence \: proved$

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