Solve 72n^4-200m^2

$$72 n ^ { 4 } - 200 m ^ { 2 }$$

Factor

$$8\left(3n^{2}-5m\right)\left(5m+3n^{2}\right)$$

Solution Steps

Factor out 8.

$$8\left(9n^{4}-25m^{2}\right)$$

Consider 9n^{4}-25m^{2}. Rewrite 9n^{4}-25m^{2} as \left(3n^{2}\right)^{2}-\left(5m\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3n^{2}-5m\right)\left(3n^{2}+5m\right)$$

Reorder the terms.

$$\left(-5m+3n^{2}\right)\left(5m+3n^{2}\right)$$

Rewrite the complete factored expression.

$$8\left(-5m+3n^{2}\right)\left(5m+3n^{2}\right)$$

Evaluate

$$72n^{4}-200m^{2}$$