Solve a^2+4a+4-9b^2

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

Factor

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

Solution Steps

Rewrite a^{2}+4a+4-9b^{2} as \left(2+a\right)^{2}-\left(3b\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Reorder the terms.

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

Evaluate

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