Solve 15-5m^2-3r^2+m^2r^2

$$15 - 5 m ^ { 2 } - 3 r ^ { 2 } + m ^ { 2 } r ^ { 2 }$$

Factor

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

Solution Steps

Do the grouping 15-5m^{2}-3r^{2}+m^{2}r^{2}=\left(15-5m^{2}\right)+\left(-3r^{2}+m^{2}r^{2}\right), and factor out -5 in the first and r^{2} in the second group.

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

Factor out common term m^{2}-3 by using distributive property. The following polynomials are not factored since they do not have any rational roots: r^{2}-5,m^{2}-3.

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

Evaluate

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