Question

factorise the following -
1. a⁷+ab⁶​

Answer 1

$a^{7}+ab^{6}$

Taking a as common,

$a(a^{6}+b^{6})\\=a[(a^{2})^{3}+(b^{2})^{3}]$

Applying the identity $(a^{3}+b^{3})=(a+b)(a^{2}-ab+b^{2})$,

$=a[(a^{2}+b^{2})(a^{4}-a^{2}b^{2}+b^{4})\\=a(a^{2}+b^{2})(a^{4}-a^{2}b^{2}+b^{4})$

Therefore, your answer is $a(a^{2}+b^{2})(a^{4}-a^{2}b^{2}+b^{4})$.

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