Question

How do you factor `y=3x^3-300x`?

Answer 1

`y = 3x(x^2 - 100)`

Explanation:

There is at least one `x` on every term at the right so you can already factorize by `x`, which gives you `y = x(3x^2 + 300)`.

But 300 and 3 both have 3 as common divisor, so you can also say that `y = 3x(x^2 - 100)`. I hope that answers your question.

Answer 2

`y=3x(x-10)(x+10)`

Explanation:

Factoring out `3x` gives:

`y=3x(x^2-100)`

But `100` is `10^2` giving:

`y=3x(x^2-10^2)`

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

Applying this to our question gives:

`y=3x(x-10)(x+10)`