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(6x2y–8xy+7xy2)+(3xy2–2x2y+xy)

2 min read Jun 16, 2024
(6x2y–8xy+7xy2)+(3xy2–2x2y+xy)

Simplifying Algebraic Expressions: (6x²y–8xy+7xy²)+(3xy²–2x²y+xy)

This article will guide you through the process of simplifying the given algebraic expression: (6x²y–8xy+7xy²)+(3xy²–2x²y+xy)

Understanding the Basics

Before we begin, let's refresh some basic concepts:

  • Algebraic Expressions: These are combinations of variables (letters) and constants (numbers) connected by mathematical operations (addition, subtraction, multiplication, etc.).
  • Like Terms: Terms with the same variables raised to the same powers are considered like terms. For instance, 4xy² and -2xy² are like terms, while 4xy² and 4x²y are not.

Simplifying the Expression

  1. Identify Like Terms: In our expression, we have:

    • x²y terms: 6x²y and -2x²y
    • xy terms: -8xy and xy
    • xy² terms: 7xy² and 3xy²

  2. Combine Like Terms: Add or subtract the coefficients of the like terms.

    • x²y terms: 6x²y - 2x²y = 4x²y
    • xy terms: -8xy + xy = -7xy
    • xy² terms: 7xy² + 3xy² = 10xy²

  3. Combine the Simplified Terms: The simplified expression is the sum of the combined like terms: 4x²y - 7xy + 10xy²

Conclusion

The simplified form of the algebraic expression (6x²y–8xy+7xy²)+(3xy²–2x²y+xy) is 4x²y - 7xy + 10xy². By identifying and combining like terms, we have effectively simplified the expression.

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