Solve -t(2t^3+3t^2-5t)=

$$- t ( 2 t ^ { 3 } + 3 t ^ { 2 } - 5 t ) =$$

Evaluate

$$-\left(t-1\right)\left(2t+5\right)t^{2}$$

Solution Steps

Use the distributive property to multiply -t by 2t^{3}+3t^{2}-5t.

$$2\left(-t\right)t^{3}+3\left(-t\right)t^{2}-5\left(-t\right)t$$

Multiply -5 and -1 to get 5.

$$2\left(-t\right)t^{3}+3\left(-t\right)t^{2}+5tt$$

Multiply t and t to get t^{2}.

$$2\left(-t\right)t^{3}+3\left(-t\right)t^{2}+5t^{2}$$

Multiply 2 and -1 to get -2.

$$-2tt^{3}+3\left(-1\right)tt^{2}+5t^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$-2t^{4}+3\left(-1\right)tt^{2}+5t^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-2t^{4}+3\left(-1\right)t^{3}+5t^{2}$$

Multiply 3 and -1 to get -3.

$$-2t^{4}-3t^{3}+5t^{2}$$

Expand

$$5t^{2}-3t^{3}-2t^{4}$$

Solution Steps

Use the distributive property to multiply -t by 2t^{3}+3t^{2}-5t.

$$2\left(-t\right)t^{3}+3\left(-t\right)t^{2}-5\left(-t\right)t$$

Multiply -5 and -1 to get 5.

$$2\left(-t\right)t^{3}+3\left(-t\right)t^{2}+5tt$$

Multiply t and t to get t^{2}.

$$2\left(-t\right)t^{3}+3\left(-t\right)t^{2}+5t^{2}$$

Multiply 2 and -1 to get -2.

$$-2tt^{3}+3\left(-1\right)tt^{2}+5t^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$-2t^{4}+3\left(-1\right)tt^{2}+5t^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-2t^{4}+3\left(-1\right)t^{3}+5t^{2}$$

Multiply 3 and -1 to get -3.

$$-2t^{4}-3t^{3}+5t^{2}$$