(3x^2-5xy^2y^3)+(-3x^2-5xy^2y^3)

2 min read Jun 16, 2024

Simplifying Algebraic Expressions: (3x^2 - 5xy^2y^3) + (-3x^2 - 5xy^2y^3)

This article will guide you through simplifying the algebraic expression: (3x^2 - 5xy^2y^3) + (-3x^2 - 5xy^2y^3).

The expression consists of two sets of terms enclosed in parentheses. Each set contains:

Variables: 'x' and 'y' representing unknown quantities.
Coefficients: Numbers multiplying the variables (3 and -5).
Exponents: Powers indicating how many times a variable is multiplied by itself (2 and 3).

To simplify, we can follow these steps:

Remove the parentheses: Since we're adding the sets, the parentheses don't affect the order of operations. We can rewrite the expression as: 3x^2 - 5xy^2y^3 - 3x^2 - 5xy^2y^3
Combine like terms: Like terms are those with the same variables raised to the same exponents. In our case, we have:
- 3x^2 - 3x^2: These terms cancel each other out.
- -5xy^2y^3 - 5xy^2y^3: These terms combine to give -10xy^2y^3
Simplify the expression: After combining, we're left with: -10xy^2y^3

The simplified expression of (3x^2 - 5xy^2y^3) + (-3x^2 - 5xy^2y^3) is -10xy^2y^3.

Remember, we can further simplify the exponents: y^2 * y^3 = y^(2+3) = y^5. Therefore, the final simplified expression is -10xy^5.