Solve s(t)=-2(t-1)(t-2)^2-3

$$s ( t ) = - 2 ( t - 1 ) ( t - 2 ) ^ { 2 } - 3$$

Evaluate

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

Solution Steps

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

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

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

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

Use the distributive property to multiply -2t+2 by t^{2}-4t+4 and combine like terms.

$$-2t^{3}+10t^{2}-16t+8-3$$

Subtract 3 from 8 to get 5.

$$-2t^{3}+10t^{2}-16t+5$$

Expand

$$5-16t+10t^{2}-2t^{3}$$

Solution Steps

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

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

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

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

Use the distributive property to multiply -2t+2 by t^{2}-4t+4 and combine like terms.

$$-2t^{3}+10t^{2}-16t+8-3$$

Subtract 3 from 8 to get 5.

$$-2t^{3}+10t^{2}-16t+5$$