Solve (a+3b)^2-3(a+3b)-4

$$( a + 3 b ) ^ { 2 } - 3 ( a + 3 b ) - 4$$

Evaluate

$$\left(a+3b-4\right)\left(a+3b+1\right)$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+3b\right)^{2}.

$$a^{2}+6ab+9b^{2}-3\left(a+3b\right)-4$$

Use the distributive property to multiply -3 by a+3b.

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

Expand

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

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+3b\right)^{2}.

$$a^{2}+6ab+9b^{2}-3\left(a+3b\right)-4$$

Use the distributive property to multiply -3 by a+3b.

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