(-9v^2-8u)+(-2uv-2u^2+v^2)+(-v^2+4uv)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions

This article will guide you through the process of simplifying the algebraic expression: (-9v^2 - 8u) + (-2uv - 2u^2 + v^2) + (-v^2 + 4uv)

Understanding the Expression

The given expression involves several terms with different variables and exponents. To simplify it, we need to combine like terms.

Like terms are terms that have the same variable(s) raised to the same power. For example, -9v^2 and v^2 are like terms because they both have the variable v raised to the power of 2.

Steps to Simplify

1. Remove the parentheses: Since we are adding the terms, the parentheses don't affect the order of operations. We can simply rewrite the expression without them:

   -9v^2 - 8u - 2uv - 2u^2 + v^2 - v^2 + 4uv

2. Identify like terms: Group together the terms with the same variables and exponents:

   (-9v^2 + v^2 - v^2) + (-8u) + (-2uv + 4uv) - 2u^2

3. Combine like terms: Perform the arithmetic operations on the coefficients of each group:

   -9v^2 + (-8u) + 2uv - 2u^2

4. Rearrange the terms: It's customary to write expressions in descending order of exponents, and then alphabetically by variable.

   -2u^2 - 8u + 2uv - 9v^2

Simplified Expression

The simplified expression is: -2u^2 - 8u + 2uv - 9v^2