How do you factor the expression $16x^3 + 54y^6$ ?

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Answer 1 · 2015-12-20T18:27:52

Factor out a $2$ and apply the sum of cubes formula to find that

$16x^3 + 54y^6= 2(2x + 3y^2)(4x^2 - 6xy^2 + 9y^4)$

The sum of cubes formula states that

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

(verify this by expanding the right hand side)

With this available, we have

$16x^3 + 54y^6 = 2(8x^3 + 27y^6)$

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

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

(applying the sum of cubes formula)

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

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

How do you factor the expression 16x^3 + 54y^616x^3 + 54y^6?