How do you factor $8x^3y^6-125$ ?

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Answer 1 · 2016-01-03T06:54:10

$(2xy^2-5)(2x^2y^4+10xy^2+25)$

This is a difference of cubes, which takes the general form:

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

Recognize that $8x^3y^6=(2xy^2)^3$ and that $125=5^3$ .

$(2xy^2)^3-5^3=(2xy^2-5)((2xy^2)^2+2xy^2(5)+5^2)$

$=(2xy^2-5)(2x^2y^4+10xy^2+25)$

How do you factor 8x^3y^6-1258x^3y^6-125?