To simplify the expression [tex]\(3y^2 + 2xy + 1 + 3x + y + 2x^2\)[/tex], we follow these steps:
1. Rewrite the expression to group like terms together (terms with the same powers of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]):
[tex]\[
3y^2 + 2xy + y + 2x^2 + 3x + 1
\][/tex]
2. Combine like terms. Since there are no other terms that can be combined (each term has a different combination or power of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]), the expression remains the same:
[tex]\[
3y^2 + 2xy + y + 2x^2 + 3x + 1
\][/tex]
3. Arrange the terms in a standard polynomial order (commonly in descending powers of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]):
[tex]\[
2x^2 + 2xy + 3x + 3y^2 + y + 1
\][/tex]
This is the simplified form of the expression.
