To simplify the expression [tex]\(4xy^2 + 3x^2 + 2y + 5xy^2 + 7y\)[/tex], we need to combine like terms. Let's break it down and group the like terms together.
1. Identify like terms:
- Terms involving [tex]\(x^2\)[/tex]
- Terms involving [tex]\(xy^2\)[/tex]
- Terms involving only [tex]\(y\)[/tex]
2. Group the like terms:
[tex]\[
4xy^2 + 5xy^2 + 3x^2 + 2y + 7y
\][/tex]
3. Combine the like terms:
- For the [tex]\(xy^2\)[/tex] terms:
[tex]\[
4xy^2 + 5xy^2 = 9xy^2
\][/tex]
- For the [tex]\(x^2\)[/tex] term, there is only one term:
[tex]\[
3x^2
\][/tex]
- For the [tex]\(y\)[/tex] terms:
[tex]\[
2y + 7y = 9y
\][/tex]
4. Write down the simplified expression with the combined like terms:
[tex]\[
3x^2 + 9xy^2 + 9y
\][/tex]
Therefore, the simplified form of the given expression [tex]\(4xy^2 + 3x^2 + 2y + 5xy^2 + 7y\)[/tex] is:
[tex]\[
3x^2 + 9xy^2 + 9y
\][/tex]
