Solve 9w^4-9z^4

$$9 w ^ { 4 } - 9 z ^ { 4 }$$

Factor

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

Solution Steps

Factor out 9.

$$9\left(w^{4}-z^{4}\right)$$

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

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

Reorder the terms.

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

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

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

Reorder the terms.

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

Rewrite the complete factored expression.

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

Evaluate

$$9\left(w^{4}-z^{4}\right)$$