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

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

Evaluate

$$-\left(3-2b\right)^{2}+a^{2}$$

Solution Steps

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

$$a^{2}+2ab-3a-2ba-4b^{2}+6b+3a+6b-9$$

Combine 2ab and -2ba to get 0.

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

Combine -3a and 3a to get 0.

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

Combine 6b and 6b to get 12b.

$$a^{2}-4b^{2}+12b-9$$

Expand

$$a^{2}-4b^{2}+12b-9$$

Solution Steps

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

$$a^{2}+2ab-3a-2ba-4b^{2}+6b+3a+6b-9$$

Combine 2ab and -2ba to get 0.

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

Combine -3a and 3a to get 0.

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

Combine 6b and 6b to get 12b.

$$a^{2}-4b^{2}+12b-9$$