Question

How do you factor `2x^3-18x`?

Answer 1

`2x^3-18x = 2x(x-3)(x+3)`

Explanation:

Separate out the common factor `2x`, then use the difference of squares identity:

`a^2-b^2 = (a-b)(a+b)`

with `a=x` and `b=3` as follows:

`2x^3-18x = 2x(x^2-9)`

`color(white)(2x^3-18x) = 2x(x^2-3^2)`

`color(white)(2x^3-18x) = 2x(x-3)(x+3)`