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Question
Factorize each of the following expression:
(x + 2y)2 − 4(2x − y)2
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Solution
\[(x + 2y )^2 - 4(2x - y )^2 = (x + 2y )^2 - [2(2x - y) ]^2 \]
\[ = [(x + 2y) - 2(2x - y)][(x + 2y) + 2(2x - y)]\]
\[ = (x + 2y - 4x + 2y)(x + 2y + 4x - 2y)\]
\[ = 5x(4y - 3x)\]
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