(x%2B2)-(2x-1)(x-6).jpeg "(x+3)(x+2)-(2x-1)(x-6)")
Expanding and Simplifying the Expression: (x+3)(x+2)-(2x-1)(x-6)
This article will walk through the process of expanding and simplifying the algebraic expression: (x+3)(x+2)-(2x-1)(x-6)
Expanding the Expression
First, we will expand each of the two products using the FOIL method (First, Outer, Inner, Last):
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(x+3)(x+2)
- First: x * x = x²
- Outer: x * 2 = 2x
- Inner: 3 * x = 3x
- Last: 3 * 2 = 6
- Combining terms: x² + 2x + 3x + 6 = x² + 5x + 6
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(2x-1)(x-6)
- First: 2x * x = 2x²
- Outer: 2x * -6 = -12x
- Inner: -1 * x = -x
- Last: -1 * -6 = 6
- Combining terms: 2x² -12x -x + 6 = 2x² - 13x + 6
Now we have the expanded form: x² + 5x + 6 - (2x² - 13x + 6)
Simplifying the Expression
We can simplify further by distributing the negative sign:
x² + 5x + 6 - 2x² + 13x - 6
Finally, combine like terms:
(x² - 2x²) + (5x + 13x) + (6 - 6)
-x² + 18x
Final Result
The simplified form of the expression (x+3)(x+2)-(2x-1)(x-6) is -x² + 18x.