how do you factor a binomial?

64-x^3

this is a difference of 2 cubes
64 = 4³
and x³ obvioulsy = x³

to factor the difference of 2 cubes, apply the following formula:

a³-b³ = (a-b)(a²+ab+b²)
a = 4
b = x

64 - x³ = (4 - x)(16 + 4x + x²) <--final answer

That's not a binomial.
Cube factorization.

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

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

This is the difference of two cubes:

The rule here is:
a³ - b³ = (a - b)(a² + ab + b²)

So 64 - x³ factors out to:

(4 - x)(16 + 4x + x²)

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

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

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