Is it possible to factor y= 2x^3-50x ? If so, what are the factors?

Mar 9, 2018

$y = 2 x \left(x + 5\right) \left(x - 5\right)$

Explanation:

Well, we can already see that both terms have an $x$, and are a multiple of $2$ so we can take $2 x$ out to get $y = 2 x \left({x}^{2} - 25\right)$

Difference of two squares tell us that ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$.

${x}^{2} - 25 = \left(x + 5\right) \left(x - 5\right)$ since ${x}^{2} = {\left(x\right)}^{2}$ and $25 = {5}^{2}$

This gives us $y = 2 x \left(\left(x + 5\right) \left(x - 5\right)\right) = 2 x \left(x + 5\right) \left(x - 5\right)$