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)
StepbyStep Breakdown:

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

Combine like terms: Add the coefficients of the like terms:
 (5 + 2)x³y² = 7x³y²
 (3 + 4)xy = xy
 2  7 = 5

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.