To find a detailed step-by-step solution for the expression [tex]\(3x^2y - 5xy^2 + x - 3y + 2\)[/tex], we need to understand and simplify each term.
The given expression is a polynomial in two variables, [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. Let's examine each term:
1. First Term: [tex]\(3x^2y\)[/tex]
- This term consists of a coefficient [tex]\(3\)[/tex], the variable [tex]\(x\)[/tex] raised to the power of [tex]\(2\)[/tex], and the variable [tex]\(y\)[/tex].
2. Second Term: [tex]\(-5xy^2\)[/tex]
- This term consists of a coefficient [tex]\(-5\)[/tex], the variable [tex]\(x\)[/tex], and the variable [tex]\(y\)[/tex] raised to the power of [tex]\(2\)[/tex].
3. Third Term: [tex]\(x\)[/tex]
- This is a linear term in [tex]\(x\)[/tex].
4. Fourth Term: [tex]\(-3y\)[/tex]
- This is a linear term in [tex]\(y\)[/tex] with a coefficient of [tex]\(-3\)[/tex].
5. Fifth Term: [tex]\(2\)[/tex]
- This is a constant term.
So, the full expression is a combination of these terms:
[tex]\[
3x^2y - 5xy^2 + x - 3y + 2
\][/tex]
Every term is already simplified, and there are no like terms to combine. Therefore, the given polynomial expression is already in its simplest form.
Thus, the expression [tex]\(3x^2y - 5xy^2 + x - 3y + 2\)[/tex] is the simplified form.
This is the final answer:
[tex]\[
3x^2y - 5xy^2 + x - 3y + 2
\][/tex]
