Solve {l}{(10-4t)^2}{+36t^2}

$$\left. \begin{array} { l } { ( 10 - 4 t ) ^ { 2 } } \\ { + 36 t ^ { 2 } } \end{array} \right.$$

Evaluate

$$52t^{2}-80t+100$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10-4t\right)^{2}.

$$100-80t+16t^{2}+36t^{2}$$

Combine 16t^{2} and 36t^{2} to get 52t^{2}.

$$100-80t+52t^{2}$$

Expand

$$52t^{2}-80t+100$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10-4t\right)^{2}.

$$100-80t+16t^{2}+36t^{2}$$

Combine 16t^{2} and 36t^{2} to get 52t^{2}.

$$100-80t+52t^{2}$$