Solve (a+3/2)^2-1/2

$$( a + \frac { 3 } { 2 } ) ^ { 2 } - \frac { 1 } { 2 }$$

Evaluate

$$a^{2}+3a+\frac{7}{4}$$

Solution Steps

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

$$a^{2}+3a+\frac{9}{4}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{9}{4} to get \frac{7}{4}.

$$a^{2}+3a+\frac{7}{4}$$

Expand

$$a^{2}+3a+\frac{7}{4}$$

Solution Steps

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

$$a^{2}+3a+\frac{9}{4}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{9}{4} to get \frac{7}{4}.

$$a^{2}+3a+\frac{7}{4}$$