%2B(3xy%5E2%E2%80%932x%5E2y%2Bxy).jpeg "(6x^2y–8xy+7xy^2)+(3xy^2–2x^2y+xy)")
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.