Solve (a-2b+c+3)(a+2b-c+3)

$$( a - 2 b + c + 3 ) ( a + 2 b - c + 3 )$$

Evaluate

$$-\left(c-2b\right)^{2}+a^{2}+6a+9$$

Solution Steps

Apply the distributive property by multiplying each term of a-2b+c+3 by each term of a+2b-c+3.

$$a^{2}+2ab-ac+3a-2ba-4b^{2}+2bc-6b+ca+2cb-c^{2}+3c+3a+6b-3c+9$$

Combine 2ab and -2ba to get 0.

$$a^{2}-ac+3a-4b^{2}+2bc-6b+ca+2cb-c^{2}+3c+3a+6b-3c+9$$

Combine -ac and ca to get 0.

$$a^{2}+3a-4b^{2}+2bc-6b+2cb-c^{2}+3c+3a+6b-3c+9$$

Combine 2bc and 2cb to get 4bc.

$$a^{2}+3a-4b^{2}+4bc-6b-c^{2}+3c+3a+6b-3c+9$$

Combine 3a and 3a to get 6a.

$$a^{2}+6a-4b^{2}+4bc-6b-c^{2}+3c+6b-3c+9$$

Combine -6b and 6b to get 0.

$$a^{2}+6a-4b^{2}+4bc-c^{2}+3c-3c+9$$

Combine 3c and -3c to get 0.

$$a^{2}+6a-4b^{2}+4bc-c^{2}+9$$

Expand

$$a^{2}+6a-4b^{2}+4bc-c^{2}+9$$

Solution Steps

Apply the distributive property by multiplying each term of a-2b+c+3 by each term of a+2b-c+3.

$$a^{2}+2ab-ac+3a-2ba-4b^{2}+2bc-6b+ca+2cb-c^{2}+3c+3a+6b-3c+9$$

Combine 2ab and -2ba to get 0.

$$a^{2}-ac+3a-4b^{2}+2bc-6b+ca+2cb-c^{2}+3c+3a+6b-3c+9$$

Combine -ac and ca to get 0.

$$a^{2}+3a-4b^{2}+2bc-6b+2cb-c^{2}+3c+3a+6b-3c+9$$

Combine 2bc and 2cb to get 4bc.

$$a^{2}+3a-4b^{2}+4bc-6b-c^{2}+3c+3a+6b-3c+9$$

Combine 3a and 3a to get 6a.

$$a^{2}+6a-4b^{2}+4bc-6b-c^{2}+3c+6b-3c+9$$

Combine -6b and 6b to get 0.

$$a^{2}+6a-4b^{2}+4bc-c^{2}+3c-3c+9$$

Combine 3c and -3c to get 0.

$$a^{2}+6a-4b^{2}+4bc-c^{2}+9$$