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

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

Evaluate

$$-2t^{3}-2t^{2}-27t-9$$

Solution Steps

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

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

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

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

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

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

Combine 18t and -45t to get -27t.

$$3t^{3}-2t^{2}-27t-9+5\left(-t^{3}\right)$$

Multiply 5 and -1 to get -5.

$$3t^{3}-2t^{2}-27t-9-5t^{3}$$

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

$$-2t^{3}-2t^{2}-27t-9$$

Expand

$$-2t^{3}-2t^{2}-27t-9$$

Solution Steps

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

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

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

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

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

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

Combine 18t and -45t to get -27t.

$$3t^{3}-2t^{2}-27t-9+5\left(-t^{3}\right)$$

Multiply 5 and -1 to get -5.

$$3t^{3}-2t^{2}-27t-9-5t^{3}$$

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

$$-2t^{3}-2t^{2}-27t-9$$