Solve 80w^4v^2-5v^2

$$80 w ^ { 4 } v ^ { 2 } - 5 v ^ { 2 }$$

Factor

$$5\left(2w-1\right)\left(2w+1\right)v^{2}\left(4w^{2}+1\right)$$

Solution Steps

Factor out 5.

$$5\left(16w^{4}v^{2}-v^{2}\right)$$

Consider 16w^{4}v^{2}-v^{2}. Factor out v^{2}.

$$v^{2}\left(16w^{4}-1\right)$$

Consider 16w^{4}-1. Rewrite 16w^{4}-1 as \left(4w^{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).

$$\left(4w^{2}-1\right)\left(4w^{2}+1\right)$$

Consider 4w^{2}-1. Rewrite 4w^{2}-1 as \left(2w\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).

$$\left(2w-1\right)\left(2w+1\right)$$

Rewrite the complete factored expression. Polynomial 4w^{2}+1 is not factored since it does not have any rational roots.

$$5v^{2}\left(2w-1\right)\left(2w+1\right)\left(4w^{2}+1\right)$$

Evaluate

$$5v^{2}\left(16w^{4}-1\right)$$