(x-1)(x-2).jpeg "(x+6)(x-1)(x-2)")
Expanding and Simplifying (x+6)(x-1)(x-2)
This expression represents the product of three binomials. To understand it better, we can expand it step by step.
Step 1: Expanding the first two binomials
First, we expand (x+6)(x-1) using the FOIL method:
- First: x * x = x²
- Outer: x * -1 = -x
- Inner: 6 * x = 6x
- Last: 6 * -1 = -6
Combining the terms, we get:
(x+6)(x-1) = x² -x + 6x -6 = x² + 5x - 6
Step 2: Expanding the result with the third binomial
Now, we multiply the result from step 1 (x² + 5x - 6) with (x-2):
We can use the distributive property to do this:
- x² * (x-2) = x³ - 2x²
- 5x * (x-2) = 5x² - 10x
- -6 * (x-2) = -6x + 12
Combining all the terms, we get:
(x² + 5x - 6)(x-2) = x³ - 2x² + 5x² - 10x - 6x + 12
Finally, simplifying by combining like terms:
(x+6)(x-1)(x-2) = x³ + 3x² - 16x + 12
Conclusion
Therefore, the expanded and simplified form of (x+6)(x-1)(x-2) is x³ + 3x² - 16x + 12. This expression represents a cubic polynomial with a leading coefficient of 1.