How do you factor $27a^3-64b^3$ ?

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Answer 1 · 2016-01-08T12:10:10

$27a^3-64b^3=(3a-4b)(9a^2+12ab+16b^2)$

Remembering that:

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

we can try to write

$27a^3-64b^3$

like a difference of cubes

$27a^3-64b^3=3^3a^3-2^6b^3=3^3a^3-(2^2)^3b^3=$
$(3a)^3-4^3b^3=(3a)^3-(4b)^3$

Now we can apply the rule:

$27a^3-64b^3=(3a)^3-(4b)^3=$
$=(3a-4b)((3a)^2+12ab+(4b)^2)$
$=(3a-4b)(9a^2+12ab+16b^2)$

How do you factor 27a^3-64b^327a^3-64b^3?