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Multiplication of Any Polynomial

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Question

Evaluate: $(x + y) (2 x + y) (2 x - y) (x - y)$

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Solution

$(x + y) (2 x + y) (2 x - y) (x - y)$
$= (x + y) (x - y) (2 x + y) (2 x - y)$
$= (x^{2} - y^{2}) (4 x^{2} - y^{2})$ using $(a + b) (a - b) = a^{2} - b^{2}$
$= x^{2} (4 x^{2} - y^{2}) - y^{2} (4 x^{2} - y^{2})$
$= 4 x^{4} - x^{2} y^{2} - 4 x^{2} y^{2} + y^{4}$
$= 4 x^{4} - 5 x^{2} y^{2} + y^{4}$

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