(6x+3)-(2x-5)(2x+1)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (6x+3)-(2x-5)(2x+1)

This article will guide you through the process of simplifying the expression (6x+3)-(2x-5)(2x+1).

Understanding the Steps

The expression involves both addition and multiplication, so we'll need to follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets: We need to simplify the multiplication within the parentheses first.
2. Exponents/Orders: There are no exponents in this expression.
3. Multiplication and Division: We'll multiply the terms within the parentheses.
4. Addition and Subtraction: Finally, we'll combine the terms through addition and subtraction.

Step-by-Step Solution

1. Multiply the terms inside the parentheses:

   (2x-5)(2x+1) = 4x² + 2x - 10x - 5

2. Combine like terms:

   4x² + 2x - 10x - 5 = 4x² - 8x - 5

3. Substitute the simplified expression back into the original expression:

   (6x+3)-(2x-5)(2x+1) = (6x+3) - (4x² - 8x - 5)

4. Distribute the negative sign:

   (6x+3) - (4x² - 8x - 5) = 6x + 3 - 4x² + 8x + 5

5. Combine like terms:

   6x + 3 - 4x² + 8x + 5 = -4x² + 14x + 8

Final Result

The simplified expression is -4x² + 14x + 8.