(x-1)-(2x-3)(x%5E2-x%2B1).jpeg "(x^3-2x^2+3x-4)(x-1)-(2x-3)(x^2-x+1)")
Expanding and Simplifying the Expression: (x^3-2x^2+3x-4)(x-1)-(2x-3)(x^2-x+1)
This article aims to simplify the given expression by expanding and combining like terms.
Step 1: Expanding the Expressions
We begin by expanding both products in the expression:
(x^3-2x^2+3x-4)(x-1):
- Multiply each term in the first set of parentheses by each term in the second set:
- x^3 * (x-1) = x^4 - x^3
- -2x^2 * (x-1) = -2x^3 + 2x^2
- 3x * (x-1) = 3x^2 - 3x
- -4 * (x-1) = -4x + 4
(2x-3)(x^2-x+1):
- Multiply each term in the first set of parentheses by each term in the second set:
- 2x * (x^2-x+1) = 2x^3 - 2x^2 + 2x
- -3 * (x^2-x+1) = -3x^2 + 3x - 3
Step 2: Combining Like Terms
Now we have:
(x^4 - x^3 - 2x^3 + 2x^2 + 3x^2 - 3x - 4x + 4) - (2x^3 - 2x^2 + 2x - 3x^2 + 3x - 3)
Combine like terms:
- x^4 + (-1-2)x^3 + (2+3)x^2 + (-3-4)x + 4 - (2x^3 - 5x^2 + 5x -3)
Simplify:
- x^4 - 3x^3 + 5x^2 - 7x + 4 - 2x^3 + 5x^2 - 5x + 3
Step 3: Final Simplification
Combine the like terms again:
- x^4 - 5x^3 + 10x^2 - 12x + 7
Therefore, the simplified form of the expression (x^3-2x^2+3x-4)(x-1)-(2x-3)(x^2-x+1) is x^4 - 5x^3 + 10x^2 - 12x + 7.