(x%5E2-5x%2B7)-(x-1).jpeg "(x-1)(x^2-5x+7) (x-1)")
Expanding and Simplifying the Expression (x-1)(x^2-5x+7)(x-1)
This expression involves multiplying three factors together. Let's break down the steps to expand and simplify it:
Step 1: Multiply the first two factors
We start by multiplying the first two factors, (x-1) and (x^2-5x+7), using the distributive property (or FOIL method):
(x-1)(x^2-5x+7) = x(x^2-5x+7) - 1(x^2-5x+7)
Expanding this further:
= x^3 - 5x^2 + 7x - x^2 + 5x - 7
Combining like terms, we get:
= x^3 - 6x^2 + 12x - 7
Step 2: Multiply the result by the third factor
Now we need to multiply the result from Step 1, (x^3 - 6x^2 + 12x - 7), by the third factor, (x-1):
(x^3 - 6x^2 + 12x - 7)(x-1) = x(x^3 - 6x^2 + 12x - 7) - 1(x^3 - 6x^2 + 12x - 7)
Expanding:
= x^4 - 6x^3 + 12x^2 - 7x - x^3 + 6x^2 - 12x + 7
Finally, combining like terms:
= x^4 - 7x^3 + 18x^2 - 19x + 7
Conclusion
Therefore, the simplified form of the expression (x-1)(x^2-5x+7)(x-1) is x^4 - 7x^3 + 18x^2 - 19x + 7.