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Algebraic Identities

Simplify: x...

Question

Simplify: $(x + y)^{2} \times (x - y)^{2} .$

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Solution

We need to simplify $(x + y)^{2} \times (x - y)^{2}$
Lets write $(x^{2} + 2 x y + y^{2}) (x^{2} - 2 x y + y^{2})$
$= x^{2} (x^{2} - 2 x y + y^{2}) + 2 x y (x^{2} - 2 x y + y^{2}) + y^{2} (x^{2} - 2 x y + y^{2})$
$= x^{4} - 2 x^{3} y + x^{2} y^{2} + 2 x^{3} y - 4 x^{2} y^{2} + 2 x y^{3} + x^{2} y^{2} - 2 x y^{3} + y^{4}$
$= x^{4} + y^{4} - 2 x^{2} y^{2}$

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