Solve 3u^3y^4-3u^3

$$3 u ^ { 3 } y ^ { 4 } - 3 u ^ { 3 }$$

Factor

$$3\left(y-1\right)\left(y+1\right)\left(y^{2}+1\right)u^{3}$$

Solution Steps

Factor out 3.

$$3\left(u^{3}y^{4}-u^{3}\right)$$

Consider u^{3}y^{4}-u^{3}. Factor out u^{3}.

$$u^{3}\left(y^{4}-1\right)$$

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

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

Consider y^{2}-1. Rewrite y^{2}-1 as y^{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).

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

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

$$3u^{3}\left(y-1\right)\left(y+1\right)\left(y^{2}+1\right)$$

Evaluate

$$3u^{3}\left(y^{4}-1\right)$$