Solve r^4-q^4

$$r ^ { 4 } - q ^ { 4 }$$

Factor

$$\left(r-q\right)\left(q+r\right)\left(q^{2}+r^{2}\right)$$

Solution Steps

Rewrite r^{4}-q^{4} as \left(r^{2}\right)^{2}-\left(q^{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).

$$\left(r^{2}-q^{2}\right)\left(r^{2}+q^{2}\right)$$

Reorder the terms.

$$\left(-q^{2}+r^{2}\right)\left(q^{2}+r^{2}\right)$$

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

$$\left(r-q\right)\left(r+q\right)$$

Reorder the terms.

$$\left(-q+r\right)\left(q+r\right)$$

Rewrite the complete factored expression.

$$\left(-q+r\right)\left(q+r\right)\left(q^{2}+r^{2}\right)$$

Evaluate

$$r^{4}-q^{4}$$