Solve (8t^2+2-4t)^2-(-t^2-2t+7)

$$( 8 t ^ { 2 } + 2 - 4 t ) ^ { 2 } - ( - t ^ { 2 } - 2 t + 7 )$$

Evaluate

$$64t^{4}-64t^{3}+49t^{2}-14t-3$$

Solution Steps

Square 8t^{2}+2-4t.

$$64t^{4}-64t^{3}+48t^{2}-16t+4-\left(-t^{2}-2t+7\right)$$

To find the opposite of -t^{2}-2t+7, find the opposite of each term.

$$64t^{4}-64t^{3}+48t^{2}-16t+4-\left(-t^{2}\right)+2t-7$$

Combine -16t and 2t to get -14t.

$$64t^{4}-64t^{3}+48t^{2}-14t+4-\left(-t^{2}\right)-7$$

Subtract 7 from 4 to get -3.

$$64t^{4}-64t^{3}+48t^{2}-14t-3-\left(-t^{2}\right)$$

Multiply -1 and -1 to get 1.

$$64t^{4}-64t^{3}+48t^{2}-14t-3+t^{2}$$

Combine 48t^{2} and t^{2} to get 49t^{2}.

$$64t^{4}-64t^{3}+49t^{2}-14t-3$$

Expand

$$64t^{4}-64t^{3}+49t^{2}-14t-3$$

Solution Steps

Square 8t^{2}+2-4t.

$$64t^{4}-64t^{3}+48t^{2}-16t+4-\left(-t^{2}-2t+7\right)$$

To find the opposite of -t^{2}-2t+7, find the opposite of each term.

$$64t^{4}-64t^{3}+48t^{2}-16t+4-\left(-t^{2}\right)+2t-7$$

Combine -16t and 2t to get -14t.

$$64t^{4}-64t^{3}+48t^{2}-14t+4-\left(-t^{2}\right)-7$$

Subtract 7 from 4 to get -3.

$$64t^{4}-64t^{3}+48t^{2}-14t-3-\left(-t^{2}\right)$$

Multiply -1 and -1 to get 1.

$$64t^{4}-64t^{3}+48t^{2}-14t-3+t^{2}$$

Combine 48t^{2} and t^{2} to get 49t^{2}.

$$64t^{4}-64t^{3}+49t^{2}-14t-3$$