Solve 125p^2r-180b^2r

$$125 p ^ { 2 } r - 180 b ^ { 2 } r$$

Factor

$$5r\left(5p-6b\right)\left(5p+6b\right)$$

Solution Steps

Factor out 5.

$$5\left(25p^{2}r-36b^{2}r\right)$$

Consider 25p^{2}r-36b^{2}r. Factor out r.

$$r\left(25p^{2}-36b^{2}\right)$$

Consider 25p^{2}-36b^{2}. Rewrite 25p^{2}-36b^{2} as \left(5p\right)^{2}-\left(6b\right)^{2}. The difference of squares can be factored using the rule: m^{2}-n^{2}=\left(m-n\right)\left(m+n\right).

$$\left(5p-6b\right)\left(5p+6b\right)$$

Rewrite the complete factored expression.

$$5r\left(5p-6b\right)\left(5p+6b\right)$$

Evaluate

$$125rp^{2}-180rb^{2}$$