How do you factor x^3+8y^3x3+8y3?

1 Answer
Dec 17, 2015

x^3+8y^3 = (x+2y)(x^2-2xy+4y^2)x3+8y3=(x+2y)(x22xy+4y2)

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)XXX(a3+b3)=(a+b)(a2ab+b2)

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)(x3+8y3)=(x3+(2y)3)

Substituting
color(white)("XXX")color(red)(x)XXXx for color(red)(a)a
and
color(white)("XXX")color(blue)(2y)XXX2y for color(blue)(b)b
in the general form
color(white)("XXX")XXXgives the answer above.