Solve (a+2b+1)(a-2b-1)

$$( a + 2 b + 1 ) ( a - 2 b - 1 )$$

Evaluate

$$-\left(2b+1\right)^{2}+a^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of a+2b+1 by each term of a-2b-1.

$$a^{2}-2ab-a+2ba-4b^{2}-2b+a-2b-1$$

Combine -2ab and 2ba to get 0.

$$a^{2}-a-4b^{2}-2b+a-2b-1$$

Combine -a and a to get 0.

$$a^{2}-4b^{2}-2b-2b-1$$

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

$$a^{2}-4b^{2}-4b-1$$

Expand

$$a^{2}-4b^{2}-4b-1$$

Solution Steps

Apply the distributive property by multiplying each term of a+2b+1 by each term of a-2b-1.

$$a^{2}-2ab-a+2ba-4b^{2}-2b+a-2b-1$$

Combine -2ab and 2ba to get 0.

$$a^{2}-a-4b^{2}-2b+a-2b-1$$

Combine -a and a to get 0.

$$a^{2}-4b^{2}-2b-2b-1$$

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

$$a^{2}-4b^{2}-4b-1$$