How do you factor $8y^3-125$ ?

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Answer 1 · 2017-02-27T00:09:45

$8y^3 - 125 = (2y-5)(4y^2+10y+25)$

The difference of cubes identity can be written:

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

Use this with $a=2y$ and $b=5$ as follows:

$8y^3 - 125 = (2y)^3-5^3$

$color(white)(8y^3 - 125) = (2y-5)((2y)^2+(2y)(5)+5^2)$

$color(white)(8y^3 - 125) = (2y-5)(4y^2+10y+25)$

How do you factor 8y^3-1258y^3-125?