Solve 9t^3u-18t^3-3t^2u+6t^2

$$9 t ^ { 3 } u - 18 t ^ { 3 } - 3 t ^ { 2 } u + 6 t ^ { 2 }$$

Factor

$$3\left(u-2\right)\left(3t-1\right)t^{2}$$

Solution Steps

Factor out 3.

$$3\left(3t^{3}u-6t^{3}-t^{2}u+2t^{2}\right)$$

Consider 3t^{3}u-6t^{3}-t^{2}u+2t^{2}. Factor out t^{2}.

$$t^{2}\left(3tu-6t-u+2\right)$$

Consider 3tu-6t-u+2. Do the grouping 3tu-6t-u+2=\left(3tu-6t\right)+\left(-u+2\right), and factor out 3t in the first and -1 in the second group.

$$3t\left(u-2\right)-\left(u-2\right)$$

Factor out common term u-2 by using distributive property.

$$\left(u-2\right)\left(3t-1\right)$$

Rewrite the complete factored expression.

$$3t^{2}\left(u-2\right)\left(3t-1\right)$$

Evaluate

$$3\left(u-2\right)\left(3t-1\right)t^{2}$$