Solve t(2-t)^2

$$t ( 2 - t ) ^ { 2 }$$

Expand

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

Solution Steps

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

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

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

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

Evaluate

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

Solution Steps

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

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

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

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