Solve (a+b-c)(a+b+c)

$$( a + b - c ) ( a + b + c )$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of a+b-c by each term of a+b+c.

$$a^{2}+ab+ac+ba+b^{2}+bc-ca-cb-c^{2}$$

Combine ab and ba to get 2ab.

$$a^{2}+2ab+ac+b^{2}+bc-ca-cb-c^{2}$$

Combine ac and -ca to get 0.

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

Combine bc and -cb to get 0.

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

Expand

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

Solution Steps

Apply the distributive property by multiplying each term of a+b-c by each term of a+b+c.

$$a^{2}+ab+ac+ba+b^{2}+bc-ca-cb-c^{2}$$

Combine ab and ba to get 2ab.

$$a^{2}+2ab+ac+b^{2}+bc-ca-cb-c^{2}$$

Combine ac and -ca to get 0.

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

Combine bc and -cb to get 0.

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