Solve 3a+3b-left(a+bright)^2

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

Evaluate

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

Solution Steps

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

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

To find the opposite of a^{2}+2ab+b^{2}, find the opposite of each term.

$$3a+3b-a^{2}-2ab-b^{2}$$

Expand

$$3b-b^{2}+3a-2ab-a^{2}$$

Solution Steps

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

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

To find the opposite of a^{2}+2ab+b^{2}, find the opposite of each term.

$$3a+3b-a^{2}-2ab-b^{2}$$