Factorise $4ax^2 - 4ay^2 + 2bx^2 - 2by^2$ completely.

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Worked solution

1. Group terms with the common factor $x^2-y^2$.

$4ax^2-4ay^2+2bx^2-2by^2$

$=4a(x^2-y^2)+2b(x^2-y^2)$

2. Extract the common binomial factor and factorise completely.

$4a(x^2-y^2)+2b(x^2-y^2)$

$=(4a+2b)(x^2-y^2)$

$=2(2a+b)(x+y)(x-y)$

Answer

$2(2a+b)(x+y)(x-y)$

AI analysis — may contain mistakes.

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