Let's evaluate the given expression step by step:
The expression to simplify is:
[tex]\[
\frac{3x^2}{2} + (2y)^2
\][/tex]
1. Simplify each term separately:
Let's start with the first term:
[tex]\[
\frac{3x^2}{2}
\][/tex]
There is no further simplification needed for this term.
Now, consider the second term:
[tex]\[
(2y)^2
\][/tex]
Squaring the term [tex]\(2y\)[/tex]:
[tex]\[
(2y)^2 = 2^2 \cdot y^2 = 4y^2
\][/tex]
2. Combine the simplified terms:
Now that we have simplified both parts of the expression, we combine them:
[tex]\[
\frac{3x^2}{2} + 4y^2
\][/tex]
Thus, the simplified form of the expression [tex]\(\frac{3x^2}{2} + (2y)^2\)[/tex] is:
[tex]\[
\frac{3x^2}{2} + 4y^2
\][/tex]
