-(x-3).jpeg "(x^3-3x^2+x-3) (x-3)")
Expanding the Expression (x^3 - 3x^2 + x - 3)(x - 3)
This article will walk through the process of expanding the expression (x^3 - 3x^2 + x - 3)(x - 3). We'll use the distributive property (also known as FOIL) to multiply the two expressions.
Using the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
In our case, we can distribute each term in (x - 3) to each term in (x^3 - 3x^2 + x - 3):
Step 1: Multiply x by each term in the first expression:
- x * x^3 = x^4
- x * -3x^2 = -3x^3
- x * x = x^2
- x * -3 = -3x
Step 2: Multiply -3 by each term in the first expression:
- -3 * x^3 = -3x^3
- -3 * -3x^2 = 9x^2
- -3 * x = -3x
- -3 * -3 = 9
Step 3: Combine all the results: x^4 - 3x^3 + x^2 - 3x - 3x^3 + 9x^2 - 3x + 9
Step 4: Combine like terms: x^4 - 6x^3 + 10x^2 - 6x + 9
Final Result
Therefore, the expanded form of (x^3 - 3x^2 + x - 3)(x - 3) is:
(x^3 - 3x^2 + x - 3)(x - 3) = x^4 - 6x^3 + 10x^2 - 6x + 9