Solve 125m^4-20n^4

$$125 { m }^{ 4 } -20 { n }^{ 4 }$$

Factor

$$5\left(5m^{2}-2n^{2}\right)\left(5m^{2}+2n^{2}\right)$$

Solution Steps

Factor out 5.

$$5\left(25m^{4}-4n^{4}\right)$$

Consider 25m^{4}-4n^{4}. Rewrite 25m^{4}-4n^{4} as \left(5m^{2}\right)^{2}-\left(2n^{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).

$$\left(5m^{2}-2n^{2}\right)\left(5m^{2}+2n^{2}\right)$$

Rewrite the complete factored expression.

$$5\left(5m^{2}-2n^{2}\right)\left(5m^{2}+2n^{2}\right)$$

Evaluate

$$125m^{4}-20n^{4}$$