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Question
Factorise.
a4 − 2a2b2 + b4
Sum
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Solution
a4 − 2a2b2 + b4
= (a2)2 − 2a2b2 + (b2)2
Using the identity (a − b)2 = a2 − 2ab + b2
= (a2 − b2)2
Using the identity a2 − b2 = (a − b) (a + b)
= [(a − b) (a + b)]2
= (a − b)2 (a + b)2
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