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Question
Factorise the following:
(x2 + y2 – z2)2 – 4x2y2
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Solution
(x2 + y2 – z2)2 – 4x2y2
= (x2 + y2 – z2)2 – (2xy)2
= (x2 + y2 – z2 – 2xy) (x2 + y2 – z2 + 2xy)
= [(x2 + y2 – 2xy) – z2] [(x2 + y2 + 2xy) – z2]
= [(x – y)2 – z2] [(x + y)2 – z2]
= [(x – y – z) (x – y + z)] [(x + y – z) (x + y + z)]
= (x – y – z) (x – y + z) (x + y – z) (x + y + z)
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