How do you factor $27x^3+64$ ?

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Answer 1 · 2015-04-12T05:03:26

When factorising the sum of cubes, we use the formula
$a^3+b^3=(a+b)(a^2-ab+b^2)$ .

In this case of $27x3+64$ ,
$27x^3 = a^3$
$64=b^3$

Find $a$ :
$27x^3 = a^3$
$root3 (27x^3) = root3 (a^3)$
$3x = a$

Find $b$ :
$64=b^3$
$root3 64 = root3 (b^3)$
$4 = b$

Substitute $a=3x$ and $b=4$ into $(a+b)(a^2-ab+b^2)$

$(3x+4)((3x)^2 - (3x xx4) + 4^2)$

= $(3x+4)(9x^2 - 12x + 16)$

$(3x+4)(9x^2 - 12x + 16)$ is the factorised form of $27x3+64$

How do you factor 27x^3+6427x^3+64?