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Algebraic Identities

Simplify : ...

Question

Simplify : $(x - y)^{2} - 7 (x^{2} - y^{2}) + 12 (x + y)^{2}$

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Solution

$(x - y)^{2} - 7 (x^{2} - y^{2}) + 12 (x + y)^{2}$

$= x^{2} + y^{2} - 2 x y - 7 x^{2} + 7 y^{2} + 12 (x^{2} + y^{2} + 2 x y)$

$= - 6 x^{2} + 8 y^{2} - 2 x y + 12 x^{2} + 12 y^{2} + 24 x y$

$= 6 x^{2} + 20 y^{2} + 22 x y$

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