How do you factor completely x^3+64x3+64?

1 Answer
May 11, 2016

x^3+64=(x+4)(x^2-4x+16)x3+64=(x+4)(x24x+16)

Explanation:

Both x^3x3 and 64=4^364=43 are perfect squares.

So we can use the sum of cubes identity:

a^3+b^3 = (a+b)(a^2-ab+b^2)a3+b3=(a+b)(a2ab+b2)

with a=xa=x and b=4b=4 as follows:

x^3+64x3+64

=x^3+4^3=x3+43

=(x+4)(x^2-x(4)+4^2)=(x+4)(x2x(4)+42)

=(x+4)(x^2-4x+16)=(x+4)(x24x+16)