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

1 Answer
Dec 17, 2015

Answer:

#x^3+8y^3 = (x+2y)(x^2-2xy+4y^2)#

Explanation:

In general:
#color(white)("XXX")(color(red)(a)^3+color(blue)(b)^3) = (color(red)(a)+color(blue)(b))(color(red)(a)^2-color(red)(a)color(blue)(b)+color(blue)(b)^2)#

for various proofs of this see:
http://www.qc.edu.hk/math/Junior%20Secondary/sum%20of%20two%20cubes.htm

#(x^3+8y^3) = (color(red)(x)^3+color(blue)((2y))^3)#

Substituting
#color(white)("XXX")color(red)(x)# for #color(red)(a)#
and
#color(white)("XXX")color(blue)(2y)# for #color(blue)(b)#
in the general form
#color(white)("XXX")#gives the answer above.