(5x3y2−3xy+2)+(2x3y2−3x2y2+4xy−7)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

In algebra, simplifying polynomial expressions involves combining like terms to produce a more compact and manageable form. Let's work through an example:

The Expression:

(5x³y²−3xy+2) + (2x³y²−3x²y² +4xy−7)

Step-by-Step Breakdown:

1. Identify like terms: Like terms have the same variables raised to the same powers. In this expression, we have:

   • x³y² terms: 5x³y² and 2x³y²
   • xy terms: -3xy and 4xy
   • Constant terms: 2 and -7

2. Combine like terms: Add the coefficients of the like terms:

   • (5 + 2)x³y² = 7x³y²
   • (-3 + 4)xy = xy
   • 2 - 7 = -5

3. Write the simplified expression: Combine the results:

Simplified Expression: 7x³y² - 3x²y² + xy - 5

Key Takeaway: Simplifying polynomial expressions involves identifying and combining like terms. This process makes it easier to analyze and manipulate expressions in further algebraic operations.