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Question
Factorize the following expressions:
a12 + b12
Solution
= (a4)3 + (b4)3
= (a4)3 + (b4 )3
= (a4 + b4 )((a4)2 - a4 x b4 + (b4 )2) [∵ a3 + b3 = (a + b)(a2 - ab + b2 )]
= (a4 + b4 )(a8 - a4b4 + b8 )
∴ a12 + b12 = (a4 + b4)(a8 - a4b4 + b8)
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