How do you factor the expression $27x^9 + 8y^6$ ?

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Answer 1 · 2016-05-28T04:52:02

$27x^9+8y^6=(3x^3+2y^2)(9x^6-6x^3y^2+4y^4)$

$27x^9+8y^6$ is a binomial each of whose monomial is a cube. Hence we can use the identity

$(a^3+b^3)=(a+b)(a^2-ab+b^2)$

As such $27x^9+8y^6=(3x^3)^3+(2y^2)^3$

= $((3x^3)+(2y^2))((3x^3)^2-(3x^3)(2y^2)+(2y^2)^2)$

= $(3x^3+2y^2)(9x^6-6x^3y^2+4y^4)$

How do you factor the expression 27x^9 + 8y^6 27x^9 + 8y^6 ?