Solve 4s^{4}t-4s^3t^2-24s^2t^3

$$4 s ^ { 4 } t - 4 s ^ { 3 } t ^ { 2 } - 24 s ^ { 2 } t ^ { 3 }$$

Factor

$$4t\left(s-3t\right)\left(s+2t\right)s^{2}$$

Solution Steps

Factor out 4.

$$4\left(s^{4}t-s^{3}t^{2}-6s^{2}t^{3}\right)$$

Consider s^{4}t-s^{3}t^{2}-6s^{2}t^{3}. Factor out s^{2}t.

$$s^{2}t\left(s^{2}-st-6t^{2}\right)$$

Consider s^{2}-st-6t^{2}. Consider s^{2}-st-6t^{2} as a polynomial over variable s.

$$s^{2}-ts-6t^{2}$$

Find one factor of the form s^{k}+m, where s^{k} divides the monomial with the highest power s^{2} and m divides the constant factor -6t^{2}. One such factor is s-3t. Factor the polynomial by dividing it by this factor.

$$\left(s-3t\right)\left(s+2t\right)$$

Rewrite the complete factored expression.

$$4s^{2}t\left(s-3t\right)\left(s+2t\right)$$

Evaluate

$$4t\left(s-3t\right)\left(s+2t\right)s^{2}$$