(x-2)-foil-method.jpeg "(x-2)(x-2) Foil Method")
The FOIL Method: Expanding (x-2)(x-2)
The FOIL method is a popular mnemonic device used to remember the steps in multiplying two binomials. FOIL stands for First, Outer, Inner, Last, which corresponds to the order in which you multiply the terms.
Let's apply this to the expression (x-2)(x-2):
1. First: Multiply the first terms of each binomial:
- x * x = x²
2. Outer: Multiply the outer terms of the binomials:
- x * -2 = -2x
3. Inner: Multiply the inner terms of the binomials:
- -2 * x = -2x
4. Last: Multiply the last terms of each binomial:
- -2 * -2 = 4
Now, combine all the terms:
x² - 2x - 2x + 4
Finally, simplify by combining like terms:
x² - 4x + 4
Therefore, the expanded form of (x-2)(x-2) using the FOIL method is x² - 4x + 4.
Understanding the FOIL Method
The FOIL method is a visual and organized way to ensure you multiply every term in the first binomial with every term in the second binomial. It helps avoid missing terms and ensures accuracy in the expansion.
Note: The FOIL method is especially useful when dealing with binomials, which are expressions with two terms. For more complex expressions, you might need to use a more general distributive property.