Solve (m^2+3/2)^2

$$( m ^ { 2 } + \frac { 3 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{\left(2m^{2}+3\right)^{2}}{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m^{2}+\frac{3}{2}\right)^{2}.

$$\left(m^{2}\right)^{2}+3m^{2}+\frac{9}{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{4}+3m^{2}+\frac{9}{4}$$

Expand

$$m^{4}+3m^{2}+\frac{9}{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m^{2}+\frac{3}{2}\right)^{2}.

$$\left(m^{2}\right)^{2}+3m^{2}+\frac{9}{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{4}+3m^{2}+\frac{9}{4}$$