Question

factorise x6- y6 solve this

Answer 1

Answer:  The required factored form of the given expression is $(x+y)(x-y)(x^2-xy+y^2)(x^2+xy+y^2).$

Step-by-step explanation:  We are given to factorize the following expression :

$E=x^6-y^6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following factorization formulas :

$(i)~a^2-b^2=(a+b)(a-b),\\\\(ii)~a^3-b^3=(a-b)(a^2+ab+b^2),\\\\(iii)~a^3+b^3=(a+b)(a^2-ab+b^2).$

The factorization of given expression (i) is as follows :

$E\\\\=x^6-y^6\\\\=(x^3)^2-(y^3)^2\\\\=(x^3+y^3)(x^3-y^3)\\\\=(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)\\\\=(x+y)(x-y)(x^2-xy+y^2)(x^2+xy+y^2).$

Thus, the required factored form of the given expression is $(x+y)(x-y)(x^2-xy+y^2)(x^2+xy+y^2).$

Answer 2

Answer:

$x^{6}-y^{6}\\=(x-y)(x^{2}+xy+y^{2})(x+y)(x^{2}-xy+y^{2})$

Step-by-step explanation:

_______________________

Here ,we are using algebraic identities :

i) a²-b² = (a-b)(a+b)

ii)a³-b³ = (a-b)(a²+ab+b²)

iii)a³+b³ = (a+b)(a²-ab+b²)

________________________

Now,

$x^{6}-y^{6}\\=(x^{3})^{2}-(y^{3})^{2}\\=(x^{3}-y^{3})(x^{3}+y^{3})\\=(x-y)(x^{2}+xy+y^{2})(x+y)(x^{2}-xy+y^{2})$

Therefore,

$x^{6}-y^{6}\\=(x-y)(x^{2}+xy+y^{2})(x+y)(x^{2}-xy+y^{2})$

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