Solve =(a-b)^2-(a^2+b^2)

$$= ( a - b ) ^ { 2 } - ( a ^ { 2 } + b ^ { 2 } )$$

Evaluate

$$-2ab$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$a^{2}-2ab+b^{2}-\left(a^{2}+b^{2}\right)$$

To find the opposite of a^{2}+b^{2}, find the opposite of each term.

$$a^{2}-2ab+b^{2}-a^{2}-b^{2}$$

Combine a^{2} and -a^{2} to get 0.

$$-2ab+b^{2}-b^{2}$$

Combine b^{2} and -b^{2} to get 0.

$$-2ab$$

Expand

$$-2ab$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$a^{2}-2ab+b^{2}-\left(a^{2}+b^{2}\right)$$

To find the opposite of a^{2}+b^{2}, find the opposite of each term.

$$a^{2}-2ab+b^{2}-a^{2}-b^{2}$$

Combine a^{2} and -a^{2} to get 0.

$$-2ab+b^{2}-b^{2}$$

Combine b^{2} and -b^{2} to get 0.

$$-2ab$$