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

$$( 2 a ^ { 3 } + 3 a ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$4\left(a^{3}\right)^{2}+12a^{3}a+9a^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$4a^{6}+12a^{3}a+9a^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$4a^{6}+12a^{4}+9a^{2}$$

Expand

$$4a^{6}+12a^{4}+9a^{2}$$

Solution Steps

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

$$4\left(a^{3}\right)^{2}+12a^{3}a+9a^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$4a^{6}+12a^{3}a+9a^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$4a^{6}+12a^{4}+9a^{2}$$