(4x^2-5x+6)+(9x^2-2x)-(11x-3)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (4x^2 - 5x + 6) + (9x^2 - 2x) - (11x - 3)

This article will guide you through the process of simplifying the given algebraic expression: (4x^2 - 5x + 6) + (9x^2 - 2x) - (11x - 3).

Understanding the Expression

The expression involves addition and subtraction of three different polynomials:

• (4x^2 - 5x + 6): A trinomial with terms involving x², x, and a constant.
• (9x² - 2x): A binomial with terms involving x² and x.
• (11x - 3): A binomial with terms involving x and a constant.

Simplifying the Expression

To simplify the expression, we'll follow these steps:

1. Remove the parentheses: Since we are adding and subtracting, the parentheses don't affect the order of operations. We can simply remove them:

   4x^2 - 5x + 6 + 9x^2 - 2x - 11x + 3
   

2. Combine like terms: Identify terms with the same variable and exponent. For example, 4x² and 9x² are like terms, and -5x, -2x, and -11x are like terms.

   (4x² + 9x²) + (-5x - 2x - 11x) + (6 + 3)
   

3. Simplify by combining the coefficients:

   13x² - 18x + 9 
   

Final Result

The simplified form of the expression (4x^2 - 5x + 6) + (9x^2 - 2x) - (11x - 3) is 13x² - 18x + 9.