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

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

Evaluate

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

Solution Steps

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

$$4-\left(9a^{2}+12ab+4b^{2}\right)$$

To find the opposite of 9a^{2}+12ab+4b^{2}, find the opposite of each term.

$$4-9a^{2}-12ab-4b^{2}$$

Expand

$$4-4b^{2}-12ab-9a^{2}$$

Solution Steps

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

$$4-\left(9a^{2}+12ab+4b^{2}\right)$$

To find the opposite of 9a^{2}+12ab+4b^{2}, find the opposite of each term.

$$4-9a^{2}-12ab-4b^{2}$$