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14 May, 18:14

Factorise (x^2+xy) ^2 - (xy+y^2) ^2

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  1. 14 May, 18:31
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    We are given with

    (x² + xy) ² - (xy + y²) ²

    which is a difference of two square with factors of:

    [ (x² + xy) + (xy + y²) ][ (x² + xy) - (xy + y²) ]

    Simplifying:

    (x² + xy + xy + y²) (x² + xy - xy - y²)

    (x² + 2xy + y²) (x² - y²)

    Which can be further factored into:

    (x + y) ² (x + y) (x - y)

    or in simplest form:

    (x + y) ³ (x - y)
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