Question

Factorize 14x^6-45x^3y^3-14y^6

Answer 1

14x^6-45x^3y^3-14y^6

14x^6-49x^3y^3+ 4x^3y^3-14y^6
= 7x^3 (2x^3 -7y^3) + 2y^3 (2x^3 -7y^3)
= (7x^3 +2y^3) (2x^3 -7y^3)

It could be further factorised as
(a^3 +b^3)=(a+b)(a^2 -ab +b^2)
And
(a^3 -b^3) =(a-b)(a^2 +ab+b^2)


(7x^3 +2y^3)= (cbrt7 x + cbrt2 y)(cbrt49 x^2 - cbrt14xy + cbrt 4 y^2)

(2x^3 -7y^3)= (cbrt2 x -cbrt7 y)(cbrt4 x^2 + cbrt14xy + cbrt 14 y^2)

So,
It would be factorised as

(cbrt7 x + cbrt2 y)(cbrt49 x^2 - cbrt14xy + cbrt 4 y^2)(cbrt2 x -cbrt7 y)(cbrt4 x^2 + cbrt14xy + cbrt 14 y^2)