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

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

Evaluate

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

Solution Steps

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

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

Combine -2a and -2a to get -4a.

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

Combine 3ab and -3ba to get 0.

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

Combine -6b and 6b to get 0.

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

Expand

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

Solution Steps

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

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

Combine -2a and -2a to get -4a.

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

Combine 3ab and -3ba to get 0.

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

Combine -6b and 6b to get 0.

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