(x-2)(x-3)-simplify.jpeg "(x-1)(x-2)(x-3) Simplify")
Simplifying (x-1)(x-2)(x-3)
This expression represents the product of three binomials. To simplify it, we need to expand the product step-by-step.
Step 1: Expand the first two binomials
First, we multiply the first two binomials: (x-1)(x-2). We can use the FOIL method:
- First: x * x = x²
- Outer: x * -2 = -2x
- Inner: -1 * x = -x
- Last: -1 * -2 = 2
Adding these terms together, we get: (x-1)(x-2) = x² - 2x - x + 2 = x² - 3x + 2
Step 2: Multiply the result by the remaining binomial
Now, we have to multiply the simplified expression (x² - 3x + 2) by the remaining binomial (x-3):
(x² - 3x + 2)(x - 3) = x²(x-3) - 3x(x-3) + 2(x-3)
We expand this further:
- x²(x-3) = x³ - 3x²
- -3x(x-3) = -3x² + 9x
- 2(x-3) = 2x - 6
Combining all terms, we get:
x³ - 3x² - 3x² + 9x + 2x - 6 = x³ - 6x² + 11x - 6
Final Result
Therefore, the simplified form of (x-1)(x-2)(x-3) is x³ - 6x² + 11x - 6.