Question

a6-b6 how to factorise it?

Answer 1

$= {a}^{6} - {b}^{6} \\ = {( {a}^{3}) }^{2} - {( {b}^{3} )}^{2} \\ = ( {a}^{3} + {b}^{3} )( {a}^{3} - {b}^{3} )$
hope it helps you

Answer 2

Answer:

$a^{6}-b^{6}\\=(a+b)(a^{2}-ab+b^{2})(a-b)(a^{2}+ab+b^{2})$

Step-by-step explanation:

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

$By \: algebraic\: identity:\\\boxed {x^{2}-y^{2}=(x+y)(x-y)}$

$=(a+b)(a^{2}-ab+b^{2})(a-b)(a^{2}+ab+b^{2})$

$By \: algebraic \: identities:\\i) x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})\\ii)x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$

Therefore,

$a^{6}-b^{6}\\=(a+b)(a^{2}-ab+b^{2})(a-b)(a^{2}+ab+b^{2})$

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