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Question
Factorise.
x4 − (x − z)4
Sum
Solution
x4 − (x − z)4
= (x2)2 − [(x − z)2]2
Using the identity a2 − b2 = (a − b) (a + b)
= [x2 − (x − z)2] [x2 + (x − z)2]
= [x − (x − z)] [x + (x − z)] [x2 + (x − z)2]
= z (2x − z) [x2 + x2 − 2xz + z2]
= z (2x − z) (2x2 − 2xz + z2)
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