(8x2 + 2x – 6) – (5x2 – 3x + 2)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (8x² + 2x – 6) – (5x² – 3x + 2)

This article will guide you through the steps to simplify the given expression: (8x² + 2x – 6) – (5x² – 3x + 2).

Understanding the Problem

The expression involves subtracting two polynomials. To simplify it, we need to apply the distributive property and combine like terms.

Steps to Simplify

1. Distribute the negative sign: The minus sign in front of the second polynomial implies that we are subtracting each term within the parentheses.

   (8x² + 2x – 6) + (-1)(5x² – 3x + 2)

2. Multiply the second polynomial by -1:

   (8x² + 2x – 6) + (-5x² + 3x - 2)

3. Combine like terms: Group the terms with the same variable and exponent.

   (8x² - 5x²) + (2x + 3x) + (-6 - 2)

4. Simplify: Perform the operations within each group.

   3x² + 5x - 8

Solution

The simplified form of the expression (8x² + 2x – 6) – (5x² – 3x + 2) is 3x² + 5x - 8.