Question

Factorise x^12-y^12.

Answer 1

x¹²-y¹²
(x6+y6)(x6-y6)
(x6+y6)(x3+y3)(x3-y3)

Answer 2

Given that,

$x^{12}-y^{12}$

To find,

We need to find the factors of the given expression

Solution,

$x^{12}-y^{12}=(x^4)^3-(y^4)^3$

Now using the identity of $a^3-b^3=(a-b)(a^2+b^2+ab)$

$(x^4)^3-(y^4)^3=(x^4-y^4)((x^4)^2+(y^4)^2+x^4y^4)\\\\=(x^4-y^4)((x^8+y^8+x^4y^4)$

So, the factors of $x^{12}-y^{12}$ is $(x^4-y^4)((x^8+y^8+x^4y^4)$