Solve 4st(s-t)-6s^2(t-t^2)-3t^2(2s^2-s)+2st(s-t)

$$4 s t ( s - t ) - 6 s ^ { 2 } ( t - t ^ { 2 } ) - 3 t ^ { 2 } ( 2 s ^ { 2 } - s ) + 2 s t ( s - t )$$

Evaluate

$$-3st^{2}$$

Solution Steps

Use the distributive property to multiply 4st by s-t.

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

Use the distributive property to multiply 2st by s-t.

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

Use the distributive property to multiply -6s^{2} by t-t^{2}.

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

Combine 4ts^{2} and -6s^{2}t to get -2ts^{2}.

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

Use the distributive property to multiply -3t^{2} by 2s^{2}-s.

$$-2ts^{2}-4st^{2}+6s^{2}t^{2}-6t^{2}s^{2}+3t^{2}s+2ts^{2}-2st^{2}$$

Combine 6s^{2}t^{2} and -6t^{2}s^{2} to get 0.

$$-2ts^{2}-4st^{2}+3t^{2}s+2ts^{2}-2st^{2}$$

Combine -4st^{2} and 3t^{2}s to get -st^{2}.

$$-2ts^{2}-st^{2}+2ts^{2}-2st^{2}$$

Combine -2ts^{2} and 2ts^{2} to get 0.

$$-st^{2}-2st^{2}$$

Combine -st^{2} and -2st^{2} to get -3st^{2}.

$$-3st^{2}$$

Expand

$$-3st^{2}$$

Solution Steps

Use the distributive property to multiply 4st by s-t.

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

Use the distributive property to multiply 2st by s-t.

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

Use the distributive property to multiply -6s^{2} by t-t^{2}.

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

Combine 4ts^{2} and -6s^{2}t to get -2ts^{2}.

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

Use the distributive property to multiply -3t^{2} by 2s^{2}-s.

$$-2ts^{2}-4st^{2}+6s^{2}t^{2}-6t^{2}s^{2}+3t^{2}s+2ts^{2}-2st^{2}$$

Combine 6s^{2}t^{2} and -6t^{2}s^{2} to get 0.

$$-2ts^{2}-4st^{2}+3t^{2}s+2ts^{2}-2st^{2}$$

Combine -4st^{2} and 3t^{2}s to get -st^{2}.

$$-2ts^{2}-st^{2}+2ts^{2}-2st^{2}$$

Combine -2ts^{2} and 2ts^{2} to get 0.

$$-st^{2}-2st^{2}$$

Combine -st^{2} and -2st^{2} to get -3st^{2}.

$$-3st^{2}$$