Solve u^4w^4-81u^4

$$u ^ { 4 } w ^ { 4 } - 81 u ^ { 4 }$$

Factor

$$\left(w-3\right)\left(w+3\right)\left(w^{2}+9\right)u^{4}$$

Solution Steps

Factor out u^{4}.

$$u^{4}\left(w^{4}-81\right)$$

Consider w^{4}-81. Rewrite w^{4}-81 as \left(w^{2}\right)^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(w^{2}-9\right)\left(w^{2}+9\right)$$

Consider w^{2}-9. Rewrite w^{2}-9 as w^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(w-3\right)\left(w+3\right)$$

Rewrite the complete factored expression. Polynomial w^{2}+9 is not factored since it does not have any rational roots.

$$u^{4}\left(w-3\right)\left(w+3\right)\left(w^{2}+9\right)$$

Evaluate

$$u^{4}\left(w^{4}-81\right)$$