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Simplifying the Expression: (2x + 3)(x - 6) - 2x² + 3x + 30
This article will guide you through the process of simplifying the algebraic expression: (2x + 3)(x - 6) - 2x² + 3x + 30.
1. Expanding the Product
We begin by expanding the product of the two binomials: (2x + 3)(x - 6). We can do this using the FOIL method:
- First: 2x * x = 2x²
- Outer: 2x * -6 = -12x
- Inner: 3 * x = 3x
- Last: 3 * -6 = -18
Adding these terms together gives us: 2x² - 12x + 3x - 18 = 2x² - 9x - 18
2. Combining Like Terms
Now, our expression becomes: 2x² - 9x - 18 - 2x² + 3x + 30
We can combine the like terms:
- 2x² - 2x² = 0
- -9x + 3x = -6x
- -18 + 30 = 12
3. Final Simplified Expression
The simplified expression is: -6x + 12
Therefore, the simplified form of the given expression (2x + 3)(x - 6) - 2x² + 3x + 30 is -6x + 12.