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Expanding and Simplifying (x+6)(x+3)(x-5)
This article will guide you through the process of expanding and simplifying the expression (x+6)(x+3)(x-5).
Step 1: Expand the First Two Factors
Begin by expanding the first two factors, (x+6)(x+3), using the FOIL method (First, Outer, Inner, Last):
- First: x * x = x²
- Outer: x * 3 = 3x
- Inner: 6 * x = 6x
- Last: 6 * 3 = 18
Combining these terms, we get: (x+6)(x+3) = x² + 3x + 6x + 18 = x² + 9x + 18
Step 2: Multiply the Result by (x-5)
Now, multiply the simplified expression (x² + 9x + 18) by (x-5) using the distributive property:
- x² * (x-5) = x³ - 5x²
- 9x * (x-5) = 9x² - 45x
- 18 * (x-5) = 18x - 90
Step 3: Combine Like Terms
Finally, combine the like terms to obtain the fully expanded and simplified expression:
x³ - 5x² + 9x² - 45x + 18x - 90 = x³ + 4x² - 27x - 90
Conclusion
Therefore, the expanded and simplified form of (x+6)(x+3)(x-5) is x³ + 4x² - 27x - 90.