(x2y−3y2+5xy2)−(−x2y+3xy2−3y2)

Jasonbradley

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Jun 17, 2024

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Simplifying Algebraic Expressions: (x2y−3y2+5xy2)−(−x2y+3xy2−3y2)

This article will guide you through simplifying the algebraic expression: (x2y−3y2+5xy2)−(−x2y+3xy2−3y2).

Understanding the Problem

The expression involves several terms with variables 'x' and 'y' raised to different powers. We aim to simplify this expression by combining like terms.

Step-by-Step Simplification

1. Distribute the Negative Sign: Begin by distributing the negative sign in front of the second set of parentheses. Remember that multiplying a negative sign by a term changes its sign:

   (x2y−3y2+5xy2) + (x2y - 3xy2 + 3y2)

2. Identify Like Terms: Identify terms with the same variables raised to the same powers. In this case, we have:

   • x2y terms: x2y and x2y
   • xy2 terms: 5xy2 and -3xy2
   • y2 terms: -3y2 and 3y2

3. Combine Like Terms: Combine the coefficients of each set of like terms:

   (1 + 1)x2y + (5 - 3)xy2 + (-3 + 3)y2

4. Simplify: Calculate the sums and differences:

   2x2y + 2xy2 + 0y2

5. Final Result: The simplified expression is:

   2x2y + 2xy2

Conclusion

By applying the rules of algebra, we successfully simplified the given expression. This process involves distributing the negative sign, identifying like terms, combining coefficients, and simplifying the resulting expression. This step-by-step method helps to break down complex expressions into manageable parts, making them easier to understand and manipulate.