Solve 2u^4y^2-2y^2

$$2 u ^ { 4 } y ^ { 2 } - 2 y ^ { 2 }$$

Factor

$$2\left(u-1\right)\left(u+1\right)y^{2}\left(u^{2}+1\right)$$

Solution Steps

Factor out 2.

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

Consider u^{4}y^{2}-y^{2}. Factor out y^{2}.

$$y^{2}\left(u^{4}-1\right)$$

Consider u^{4}-1. Rewrite u^{4}-1 as \left(u^{2}\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(u^{2}-1\right)\left(u^{2}+1\right)$$

Consider u^{2}-1. Rewrite u^{2}-1 as u^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(u-1\right)\left(u+1\right)$$

Rewrite the complete factored expression. Polynomial u^{2}+1 is not factored since it does not have any rational roots.

$$2y^{2}\left(u-1\right)\left(u+1\right)\left(u^{2}+1\right)$$

Evaluate

$$2y^{2}\left(u^{4}-1\right)$$