Solve left(2a^2+3right)^2

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

Expand

$$4a^{4}+12a^{2}+9$$

Solution Steps

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

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

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

$$4a^{4}+12a^{2}+9$$

Evaluate

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

Solution Steps

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

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

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

$$4a^{4}+12a^{2}+9$$