Solve 18u^2+15uv-12v^2

$$18 u ^ { 2 } + 15 u v - 12 v ^ { 2 }$$

Factor

$$3\left(2u-v\right)\left(3u+4v\right)$$

Solution Steps

Factor out 3.

$$3\left(6u^{2}+5uv-4v^{2}\right)$$

Consider 6u^{2}+5uv-4v^{2}. Consider 6u^{2}+5uv-4v^{2} as a polynomial over variable u.

$$6u^{2}+5vu-4v^{2}$$

Find one factor of the form ku^{m}+n, where ku^{m} divides the monomial with the highest power 6u^{2} and n divides the constant factor -4v^{2}. One such factor is 2u-v. Factor the polynomial by dividing it by this factor.

$$\left(2u-v\right)\left(3u+4v\right)$$

Rewrite the complete factored expression.

$$3\left(2u-v\right)\left(3u+4v\right)$$

Evaluate

$$3\left(2u-v\right)\left(3u+4v\right)$$