which expression is equivalent to $(2g^{3}+4)^{2}$?\n$4g^{6}+16$\n$4g^{6}+16g^{3}+16$\n$4g^{6}+8$\n$4g^{9}+16…
which expression is equivalent to $(2g^{3}+4)^{2}$?\n$4g^{6}+16$\n$4g^{6}+16g^{3}+16$\n$4g^{6}+8$\n$4g^{9}+16g^{3}+8$
Answer
Explanation:
Step1: Apply the formula $(a + b)^2=a^{2}+2ab + b^{2}$
Here $a = 2g^{3}$ and $b = 4$. So $(2g^{3}+4)^{2}=(2g^{3})^{2}+2\times(2g^{3})\times4+4^{2}$.
Step2: Calculate each term
$(2g^{3})^{2}=2^{2}\times(g^{3})^{2}=4g^{6}$; $2\times(2g^{3})\times4 = 16g^{3}$; $4^{2}=16$.
Step3: Combine the terms
$(2g^{3}+4)^{2}=4g^{6}+16g^{3}+16$.
Answer:
$4g^{6}+16g^{3}+16$ (the second option)