Solve (2g^3+4)^2

$$( 2 g ^ { 3 } + 4 ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2g^{3}+4\right)^{2}.

$$4\left(g^{3}\right)^{2}+16g^{3}+16$$

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

$$4g^{6}+16g^{3}+16$$

Expand

$$4g^{6}+16g^{3}+16$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2g^{3}+4\right)^{2}.

$$4\left(g^{3}\right)^{2}+16g^{3}+16$$

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

$$4g^{6}+16g^{3}+16$$