Solve 3(t^3-4t^2+6t-3)+5(-t^3+2t^2+9t+11)

$$3 ( t ^ { 3 } - 4 t ^ { 2 } + 6 t - 3 ) + 5 ( - t ^ { 3 } + 2 t ^ { 2 } + 9 t + 11 )$$

Evaluate

$$46+63t-2t^{2}-2t^{3}$$

Solution Steps

Use the distributive property to multiply 3 by t^{3}-4t^{2}+6t-3.

$$3t^{3}-12t^{2}+18t-9+5\left(-t^{3}+2t^{2}+9t+11\right)$$

Use the distributive property to multiply 5 by -t^{3}+2t^{2}+9t+11.

$$3t^{3}-12t^{2}+18t-9+5\left(-t^{3}\right)+10t^{2}+45t+55$$

Combine -12t^{2} and 10t^{2} to get -2t^{2}.

$$3t^{3}-2t^{2}+18t-9+5\left(-t^{3}\right)+45t+55$$

Combine 18t and 45t to get 63t.

$$3t^{3}-2t^{2}+63t-9+5\left(-t^{3}\right)+55$$

Add -9 and 55 to get 46.

$$3t^{3}-2t^{2}+63t+46+5\left(-t^{3}\right)$$

Multiply 5 and -1 to get -5.

$$3t^{3}-2t^{2}+63t+46-5t^{3}$$

Combine 3t^{3} and -5t^{3} to get -2t^{3}.

$$-2t^{3}-2t^{2}+63t+46$$

Expand

$$46+63t-2t^{2}-2t^{3}$$

Solution Steps

Use the distributive property to multiply 3 by t^{3}-4t^{2}+6t-3.

$$3t^{3}-12t^{2}+18t-9+5\left(-t^{3}+2t^{2}+9t+11\right)$$

Use the distributive property to multiply 5 by -t^{3}+2t^{2}+9t+11.

$$3t^{3}-12t^{2}+18t-9+5\left(-t^{3}\right)+10t^{2}+45t+55$$

Combine -12t^{2} and 10t^{2} to get -2t^{2}.

$$3t^{3}-2t^{2}+18t-9+5\left(-t^{3}\right)+45t+55$$

Combine 18t and 45t to get 63t.

$$3t^{3}-2t^{2}+63t-9+5\left(-t^{3}\right)+55$$

Add -9 and 55 to get 46.

$$3t^{3}-2t^{2}+63t+46+5\left(-t^{3}\right)$$

Multiply 5 and -1 to get -5.

$$3t^{3}-2t^{2}+63t+46-5t^{3}$$

Combine 3t^{3} and -5t^{3} to get -2t^{3}.

$$-2t^{3}-2t^{2}+63t+46$$