## Simplifying Polynomials: A Step-by-Step Guide

This article will guide you through the process of simplifying the polynomial expression:

**(6x²y – 8xy + 7xy²) + (3xy² – 2x²y + xy)**

### Understanding Polynomials

A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, where the exponents of the variables are non-negative integers.

**Key Components:**

**Terms:**Each individual part of a polynomial separated by addition or subtraction. For example, in the given expression, "6x²y" and "8xy" are terms.**Coefficients:**The numerical values multiplying the variables. In "6x²y," the coefficient is 6.**Variables:**The letters representing unknown values. In "7xy²," both "x" and "y" are variables.**Exponents:**The small numbers written above the variables indicating the power to which they are raised. In "3xy²," the exponent of "y" is 2.

### Simplifying the Expression

To simplify the given expression, we combine **like terms**. Like terms have the same variables raised to the same exponents.

**Step 1:** Identify like terms in the expression:

**x²y:**6x²y and -2x²y**xy:**-8xy and xy**xy²:**7xy² and 3xy²

**Step 2:** Combine the coefficients of like terms:

**x²y:**(6 - 2)x²y = 4x²y**xy:**(-8 + 1)xy = -7xy**xy²:**(7 + 3)xy² = 10xy²

**Step 3:** Write the simplified expression:

**(6x²y – 8xy + 7xy²) + (3xy² – 2x²y + xy) = 4x²y - 7xy + 10xy²**

### Conclusion

By following the steps of identifying like terms and combining their coefficients, we successfully simplified the given polynomial expression. The final simplified form is **4x²y - 7xy + 10xy²**.