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

Dec 18, 2015

$y = 3 x \left({x}^{2} - 100\right)$

#### Explanation:

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

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

Dec 18, 2015

$y = 3 x \left(x - 10\right) \left(x + 10\right)$

#### Explanation:

Factoring out $3 x$ gives:

$y = 3 x \left({x}^{2} - 100\right)$

But $100$ is ${10}^{2}$ giving:

$y = 3 x \left({x}^{2} - {10}^{2}\right)$

Known: $\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$

Applying this to our question gives:

$y = 3 x \left(x - 10\right) \left(x + 10\right)$