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

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

Evaluate

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

Solution Steps

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

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

Multiply -1 and -1 to get 1.

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

Combine ac and -ca to get 0.

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

Combine -bc and -cb to get -2bc.

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

Multiply a and a to get a^{2}.

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

Combine -ab and ba to get 0.

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

Expand

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

Solution Steps

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

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

Multiply -1 and -1 to get 1.

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

Combine ac and -ca to get 0.

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

Combine -bc and -cb to get -2bc.

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

Multiply a and a to get a^{2}.

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

Combine -ab and ba to get 0.

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