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Question
Simplify.
(x + y) (2x + y) + (x + 2y) (x − y)
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Solution
(x + y) (2x + y) + (x + 2y) (x − y)
= x (2x + y) + y (2x + y) + x (x − y) + 2y (x − y)
= 2x2 + xy + 2xy + y2 + x2 − xy + 2xy − 2y2
= (2x2 + x2) + (y2 − 2y2) + (xy + 2xy − xy + 2xy)
= 3x2 − y2 + 4xy
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