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Question
Factorise:
a6 – b6
Sum
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Solution
We know that,
a3 + b3 = (a + b) (a2 – ab + b2) ...(1)
a3 – b3 = (a – b) (a2 + ab + b2) ...(2)
a6 – b6 = (a3)2 – (b3)2
= (a3 + b3) (a3 – b3)
= (a + b) (a2 – ab + b2) (a – b) (a2 + ab + b2)
[From (1) and (2)]
= (a + b) (a – b) (a2 – ab + b2) (a2 + ab + b2)
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Method of Factorisation : the Sum Or Difference of Two Cubes
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