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

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

Evaluate

$$2t\left(t-4\right)$$

Solution Steps

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

$$t^{2}-8t+16-\left(4-t\right)\left(t+4\right)$$

Consider \left(4-t\right)\left(t+4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$t^{2}-8t+16-\left(16-t^{2}\right)$$

To find the opposite of 16-t^{2}, find the opposite of each term.

$$t^{2}-8t+16-16+t^{2}$$

Subtract 16 from 16 to get 0.

$$t^{2}-8t+t^{2}$$

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

$$2t^{2}-8t$$

Expand

$$2t^{2}-8t$$

Solution Steps

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

$$t^{2}-8t+16-\left(4-t\right)\left(t+4\right)$$

Consider \left(4-t\right)\left(t+4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$t^{2}-8t+16-\left(16-t^{2}\right)$$

To find the opposite of 16-t^{2}, find the opposite of each term.

$$t^{2}-8t+16-16+t^{2}$$

Subtract 16 from 16 to get 0.

$$t^{2}-8t+t^{2}$$

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

$$2t^{2}-8t$$