Solve F(t-1)=(t-1)^3-5(t-1)^2-4(t-1)+20

$$F ( t - 1 ) = ( t - 1 ) ^ { 3 } - 5 ( t - 1 ) ^ { 2 } - 4 ( t - 1 ) + 20$$

Evaluate

$$\left(t-6\right)\left(t-3\right)\left(t+1\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(t-1\right)^{3}.

$$t^{3}-3t^{2}+3t-1-5\left(t-1\right)^{2}-4\left(t-1\right)+20$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(t-1\right)^{2}.

$$t^{3}-3t^{2}+3t-1-5\left(t^{2}-2t+1\right)-4\left(t-1\right)+20$$

Use the distributive property to multiply -5 by t^{2}-2t+1.

$$t^{3}-3t^{2}+3t-1-5t^{2}+10t-5-4\left(t-1\right)+20$$

Combine -3t^{2} and -5t^{2} to get -8t^{2}.

$$t^{3}-8t^{2}+3t-1+10t-5-4\left(t-1\right)+20$$

Combine 3t and 10t to get 13t.

$$t^{3}-8t^{2}+13t-1-5-4\left(t-1\right)+20$$

Subtract 5 from -1 to get -6.

$$t^{3}-8t^{2}+13t-6-4\left(t-1\right)+20$$

Use the distributive property to multiply -4 by t-1.

$$t^{3}-8t^{2}+13t-6-4t+4+20$$

Combine 13t and -4t to get 9t.

$$t^{3}-8t^{2}+9t-6+4+20$$

Add -6 and 4 to get -2.

$$t^{3}-8t^{2}+9t-2+20$$

Add -2 and 20 to get 18.

$$t^{3}-8t^{2}+9t+18$$

Expand

$$t^{3}-8t^{2}+9t+18$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(t-1\right)^{3}.

$$t^{3}-3t^{2}+3t-1-5\left(t-1\right)^{2}-4\left(t-1\right)+20$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(t-1\right)^{2}.

$$t^{3}-3t^{2}+3t-1-5\left(t^{2}-2t+1\right)-4\left(t-1\right)+20$$

Use the distributive property to multiply -5 by t^{2}-2t+1.

$$t^{3}-3t^{2}+3t-1-5t^{2}+10t-5-4\left(t-1\right)+20$$

Combine -3t^{2} and -5t^{2} to get -8t^{2}.

$$t^{3}-8t^{2}+3t-1+10t-5-4\left(t-1\right)+20$$

Combine 3t and 10t to get 13t.

$$t^{3}-8t^{2}+13t-1-5-4\left(t-1\right)+20$$

Subtract 5 from -1 to get -6.

$$t^{3}-8t^{2}+13t-6-4\left(t-1\right)+20$$

Use the distributive property to multiply -4 by t-1.

$$t^{3}-8t^{2}+13t-6-4t+4+20$$

Combine 13t and -4t to get 9t.

$$t^{3}-8t^{2}+9t-6+4+20$$

Add -6 and 4 to get -2.

$$t^{3}-8t^{2}+9t-2+20$$

Add -2 and 20 to get 18.

$$t^{3}-8t^{2}+9t+18$$