How do you factor #8x^3y^6 + 27#?

1 Answer
Apr 22, 2015

#a^3+b^3 = (a+b)(a^2-ab+b^2)#
(this is either something you already know or you can derive it by synthetic division/multiplication)

#8x^3y^6+27 = (2xy^2)^3+3^3#

So this can be factored as
#(2xy^2+3)((2xy^2)^2-(2xy^2)(3)+3^2)#
or
#(2xy^2+3)(4x^2y^4-6xy^2+9)#

You might be tempted to try to factor the second part of this but if you consider the formula for roots of a quadratic:
#(-b+-sqrt(b^2-4ac))/(2a)#

we have the square root of a negative value; so there are no Real factors available.