Solve a^2-(b-c)^2

$$a ^ { 2 } - ( b - c ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

To find the opposite of b^{2}-2bc+c^{2}, find the opposite of each term.

$$a^{2}-b^{2}+2bc-c^{2}$$

Expand

$$a^{2}-b^{2}+2bc-c^{2}$$

Solution Steps

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

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

To find the opposite of b^{2}-2bc+c^{2}, find the opposite of each term.

$$a^{2}-b^{2}+2bc-c^{2}$$