Solve 125a^2-45r^2

$$125 a ^ { 2 } - 45 r ^ { 2 }$$

Factor

$$5\left(5a-3r\right)\left(3r+5a\right)$$

Solution Steps

Factor out 5.

$$5\left(25a^{2}-9r^{2}\right)$$

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

$$\left(5a-3r\right)\left(5a+3r\right)$$

Reorder the terms.

$$\left(-3r+5a\right)\left(3r+5a\right)$$

Rewrite the complete factored expression.

$$5\left(-3r+5a\right)\left(3r+5a\right)$$

Evaluate

$$125a^{2}-45r^{2}$$