Add x2y -2xy +9y2, 7y2 -xy +x2y, 2xy +3x2y - 5y2, and 4y2 -4x2y +3xy

To add the polynomials \( x^2y - 2xy + 9y^2 \), \( 7y^2 - xy + x^2y \), \( 2xy + 3x^2y - 5y^2 \), and \( 4y^2 - 4x^2y + 3xy \), let's combine like terms step by step.

### Step 1: List all the polynomials

\[
\text{First polynomial: } x^2y - 2xy + 9y^2
\]
\[
\text{Second polynomial: } 7y^2 - xy + x^2y
\]
\[
\text{Third polynomial: } 2xy + 3x^2y - 5y^2
\]
\[
\text{Fourth polynomial: } 4y^2 - 4x^2y + 3xy
\]

### Step 2: Identify and combine like terms

- **Terms involving \( x^2y \):**
  \[
  x^2y + x^2y + 3x^2y - 4x^2y = (1 + 1 + 3 - 4)x^2y = x^2y
  \]

- **Terms involving \( xy \):**
  \[
  -2xy - xy + 2xy + 3xy = (-2 - 1 + 2 + 3)xy = 2xy
  \]

- **Terms involving \( y^2 \):**
  \[
  9y^2 + 7y^2 - 5y^2 + 4y^2 = (9 + 7 - 5 + 4)y^2 = 15y^2
  \]

### Step 3: Combine the results

Adding all the like terms together, the final expression is:
\[
x^2y + 2xy + 15y^2
\]

Would you like any further details on this solution, or do you have any questions?

Here are some related questions:
1. How can you recognize like terms in polynomials?
2. What is the standard form of a polynomial?
3. How do you subtract polynomials?
4. Can polynomials of different degrees be added together?
5. How does polynomial addition relate to functions?

**Tip:** Grouping and simplifying like terms can help make polynomial expressions easier to work with, especially in complex equations.

Learn how to add polynomials x^2y - 2xy + 9y^2, 7y^2 - xy + x^2y, 2xy + 3x^2y - 5y^2, 4y^2 - 4x^2y + 3xy step-by-step. This problem involves combining like terms and simplifying polynomial expressions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation