Question

factorise a^7-ab^6 please important

Answer 1

is the answer to the question

Answer 2

Answer:

$Factors \: of \: a^{7}-ab^{6}\\=a(a+b)(a^{2}-ab+b^{2})(a-b)(a^{2}+ab+b^{2})$

Step-by-step explanation:

$Given \: a^{7}-ab^{6}$

=$a(a^{6}-b^{6})$

=$a[(a^{3})^{2}-(b^{3})^{2}]$

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

/* By algebraic identity:

$\boxed {x^{2}-y^{2}=(x+y)(x-y)}$ */

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

/* By algebraic identity:

$\boxed {x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})}$

and

$\boxed {x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})}$ */

Therefore,

$Factors \: of \: a^{7}-ab^{6}\\=a(a+b)(a^{2}-ab+b^{2})(a-b)(a^{2}+ab+b^{2})$

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