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Question
Factorise the following:
a6 – 64
Solution
a6 – 64 = a6 – 26
= (a2)3 – (22)3 ...[a3 – b3 = (a – b) + (a2 + ab + b2)]
= (a2 – 22) [(a2)2 + (a2) (22) + (22)2]
= (a + 2) (a – 2) (a4 + 4a2 + 16)
= (a + 2) (a – 2) [(a2)2 + 42 + 8a2 – 4a2]
= (a + 2) (a – 2) [(a2 + 4)2 – (2a)2] ......{a2 – b2 = (a + b) (a – b)}
= (a + 2) (a – 2) (a2 + 4 + 2a) (a2 + 4 – 2a)
= (a + 2) (a – 2) (a2 + 2a + 4) (a2 – 2a + 4)
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