Which expression is equivalent to (2g^3 + 4)^2?

1. Identify the problem: The problem asks to find an equivalent expression for $(2g^3 + 4)^2$. This involves expanding a binomial squared.
2. Recall the binomial square formula: The formula for squaring a binomial $(a+b)^2$ is $a^2 + 2ab + b^2$.
3. Identify 'a' and 'b': In the expression $(2g^3 + 4)^2$, we have $a = 2g^3$ and $b = 4$.
4. Apply the formula: Substitute the values of 'a' and 'b' into the formula $a^2 + 2ab + b^2$:
- $a^2 = (2g^3)^2$
- $2ab = 2(2g^3)(4)$
- $b^2 = (4)^2$
5. Calculate each term:
- $a^2 = (2g^3)^2 = 2^2 \cdot (g^3)^2 = 4 \cdot g^{3 \cdot 2} = 4g^6$
- $2ab = 2 \cdot 2g^3 \cdot 4 = 16g^3$
- $b^2 = 4^2 = 16$
6. Combine the terms: Add the calculated terms together: $4g^6 + 16g^3 + 16$.
7. Compare with the options: The resulting expression $4g^6 + 16g^3 + 16$ matches one of the given options.