Solve y^6-625y^2

$$y ^ { 6 } - 625 y ^ { 2 }$$

Factor

$$\left(y-5\right)\left(y+5\right)y^{2}\left(y^{2}+25\right)$$

Solution Steps

Factor out y^{2}.

$$y^{2}\left(y^{4}-625\right)$$

Consider y^{4}-625. Rewrite y^{4}-625 as \left(y^{2}\right)^{2}-25^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y^{2}-25\right)\left(y^{2}+25\right)$$

Consider y^{2}-25. Rewrite y^{2}-25 as y^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-5\right)\left(y+5\right)$$

Rewrite the complete factored expression. Polynomial y^{2}+25 is not factored since it does not have any rational roots.

$$y^{2}\left(y-5\right)\left(y+5\right)\left(y^{2}+25\right)$$

Evaluate

$$y^{2}\left(y^{4}-625\right)$$