Solve (200-80t)^2+(120-60t)^2

$$( 200 - 80 t ) ^ { 2 } + ( 120 - 60 t ) ^ { 2 }$$

Evaluate

$$10000t^{2}-46400t+54400$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(200-80t\right)^{2}.

$$40000-32000t+6400t^{2}+\left(120-60t\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(120-60t\right)^{2}.

$$40000-32000t+6400t^{2}[phone]t+3600t^{2}$$

Add 40000 and 14400 to get 54400.

$$54400-32000t+6400t^{2}-14400t+3600t^{2}$$

Combine -32000t and -14400t to get -46400t.

$$54400-46400t+6400t^{2}+3600t^{2}$$

Combine 6400t^{2} and 3600t^{2} to get 10000t^{2}.

$$54400-46400t+10000t^{2}$$

Expand

$$10000t^{2}-46400t+54400$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(200-80t\right)^{2}.

$$40000-32000t+6400t^{2}+\left(120-60t\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(120-60t\right)^{2}.

$$40000-32000t+6400t^{2}[phone]t+3600t^{2}$$

Add 40000 and 14400 to get 54400.

$$54400-32000t+6400t^{2}-14400t+3600t^{2}$$

Combine -32000t and -14400t to get -46400t.

$$54400-46400t+6400t^{2}+3600t^{2}$$

Combine 6400t^{2} and 3600t^{2} to get 10000t^{2}.

$$54400-46400t+10000t^{2}$$