(x-2)(x-3)(x-4)-simplify.jpeg "(x-1)(x-2)(x-3)(x-4) Simplify")
Simplifying the Expression (x-1)(x-2)(x-3)(x-4)
This expression represents the product of four linear factors. To simplify it, we need to expand the product. We can do this step by step:
Step 1: Expand the first two factors
(x-1)(x-2) = x² - 3x + 2
Step 2: Expand the last two factors
(x-3)(x-4) = x² - 7x + 12
Step 3: Multiply the results from Step 1 and Step 2
(x² - 3x + 2)(x² - 7x + 12) = x⁴ - 10x³ + 35x² - 50x + 24
Therefore, the simplified form of the expression (x-1)(x-2)(x-3)(x-4) is x⁴ - 10x³ + 35x² - 50x + 24.
Key Points:
- This method involves expanding the product term by term.
- The final result is a polynomial of degree 4.
- Remember to distribute each term correctly when multiplying.
Note: This simplified form can be further analyzed for its roots (where the expression equals zero) or its behavior (how it changes with different values of x).