(x-1)-foil.jpeg "(x-1)(x-1) Foil")
Understanding the FOIL Method with (x-1)(x-1)
The FOIL method is a handy acronym that helps us remember the steps for multiplying two binomials. It stands for:
- First
- Outer
- Inner
- Last
Let's apply it to the expression (x-1)(x-1):
Step 1: First
Multiply the first terms of each binomial:
- x * x = x²
Step 2: Outer
Multiply the outer terms of the binomials:
- x * -1 = -x
Step 3: Inner
Multiply the inner terms of the binomials:
- -1 * x = -x
Step 4: Last
Multiply the last terms of the binomials:
- -1 * -1 = 1
Combining the Terms
Now, add all the results together:
x² - x - x + 1
Simplifying the Expression
Combine the like terms:
x² - 2x + 1
Therefore, (x-1)(x-1) = x² - 2x + 1 using the FOIL method.
Key Takeaways
- The FOIL method ensures we multiply all the necessary terms in a binomial multiplication.
- It helps to organize the steps and avoid missing any terms.
- Always remember to combine like terms after applying FOIL to get the simplified expression.