Solve left(8-tright)^2+left(2tright)^2

$${ \left(8-t \right) }^{ 2 } + { \left(2t \right) }^{ 2 }$$

Evaluate

$$5t^{2}-16t+64$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-t\right)^{2}.

$$64-16t+t^{2}+\left(2t\right)^{2}$$

Expand \left(2t\right)^{2}.

$$64-16t+t^{2}+2^{2}t^{2}$$

Calculate 2 to the power of 2 and get 4.

$$64-16t+t^{2}+4t^{2}$$

Combine t^{2} and 4t^{2} to get 5t^{2}.

$$64-16t+5t^{2}$$

Expand

$$5t^{2}-16t+64$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-t\right)^{2}.

$$64-16t+t^{2}+\left(2t\right)^{2}$$

Expand \left(2t\right)^{2}.

$$64-16t+t^{2}+2^{2}t^{2}$$

Calculate 2 to the power of 2 and get 4.

$$64-16t+t^{2}+4t^{2}$$

Combine t^{2} and 4t^{2} to get 5t^{2}.

$$64-16t+5t^{2}$$