Solve l^4-m^4

$$l ^ { 4 } - m ^ { 4 }$$

Factor

$$\left(l-m\right)\left(m+l\right)\left(m^{2}+l^{2}\right)$$

Solution Steps

Rewrite l^{4}-m^{4} as \left(l^{2}\right)^{2}-\left(m^{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).

$$\left(l^{2}-m^{2}\right)\left(l^{2}+m^{2}\right)$$

Reorder the terms.

$$\left(-m^{2}+l^{2}\right)\left(m^{2}+l^{2}\right)$$

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

$$\left(l-m\right)\left(l+m\right)$$

Reorder the terms.

$$\left(-m+l\right)\left(m+l\right)$$

Rewrite the complete factored expression.

$$\left(-m+l\right)\left(m+l\right)\left(m^{2}+l^{2}\right)$$

Evaluate

$$l^{4}-m^{4}$$