Solve y^5-16y

$$y ^ { 5 } - 16 y$$

Factor

$$y\left(y-2\right)\left(y+2\right)\left(y^{2}+4\right)$$

Solution Steps

Factor out y.

$$y\left(y^{4}-16\right)$$

Consider y^{4}-16. Rewrite y^{4}-16 as \left(y^{2}\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y^{2}-4\right)\left(y^{2}+4\right)$$

Consider y^{2}-4. Rewrite y^{2}-4 as y^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-2\right)\left(y+2\right)$$

Rewrite the complete factored expression. Polynomial y^{2}+4 is not factored since it does not have any rational roots.

$$y\left(y-2\right)\left(y+2\right)\left(y^{2}+4\right)$$

Evaluate

$$y\left(y^{4}-16\right)$$