Question

How do you factor ($x^3-64$)?

Answer 1

Finding the factor of the expression:

Given expression is $x^3-64$

Use the identity $a^3-b^3=(a-b)(a^2+ab+b^2)$ to factorize $x^3-64$.

$(x^3-64)$ can be written as $(x^3-4^3)$.

Put $a=x$ and $b=4$ in the identity.

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

$x^2+4x+16$ is quadratic equation and discriminant $(b^2-4ac)=-48$ which is negative.

It means $x^2+4x+16$ has no real roots.

So $x^2+4x+16$can not be factorized further.

Hence, $x^3-64$ $=(x-4)(x^2+4x+16)$.