Solve (t+1)(t-2)-t(2t-1)

$$( t + 1 ) ( t - 2 ) - t ( 2 t - 1 )$$

Evaluate

$$-t^{2}-2$$

Solution Steps

Apply the distributive property by multiplying each term of t+1 by each term of t-2.

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

Combine -2t and t to get -t.

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

Use the distributive property to multiply t by 2t-1.

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

To find the opposite of 2t^{2}-t, find the opposite of each term.

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

The opposite of -t is t.

$$t^{2}-t-2-2t^{2}+t$$

Combine t^{2} and -2t^{2} to get -t^{2}.

$$-t^{2}-t-2+t$$

Combine -t and t to get 0.

$$-t^{2}-2$$

Expand

$$-t^{2}-2$$

Solution Steps

Apply the distributive property by multiplying each term of t+1 by each term of t-2.

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

Combine -2t and t to get -t.

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

Use the distributive property to multiply t by 2t-1.

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

To find the opposite of 2t^{2}-t, find the opposite of each term.

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

The opposite of -t is t.

$$t^{2}-t-2-2t^{2}+t$$

Combine t^{2} and -2t^{2} to get -t^{2}.

$$-t^{2}-t-2+t$$

Combine -t and t to get 0.

$$-t^{2}-2$$