%5E2-foiled.jpeg "(x-2)^2 Foiled")
Foiling (x-2)^2
In algebra, FOIL is a mnemonic acronym for the steps required to multiply two binomials. It stands for First, Outer, Inner, Last. This method helps to ensure that every term in one binomial is multiplied by every term in the other binomial.
Let's apply FOIL to the expression (x-2)^2.
Step 1: Rewrite the expression
(x-2)^2 is equivalent to (x-2) * (x-2)
Step 2: Apply FOIL
- First: Multiply the first terms of each binomial: x * x = x^2
- Outer: Multiply the outer terms of the binomials: x * -2 = -2x
- Inner: Multiply the inner terms of the binomials: -2 * x = -2x
- Last: Multiply the last terms of each binomial: -2 * -2 = 4
Step 3: Combine like terms
x^2 - 2x - 2x + 4 = x^2 - 4x + 4
Therefore, the expanded form of (x-2)^2 is x^2 - 4x + 4.
Important Note: When squaring a binomial, remember that you need to multiply the entire binomial by itself. You cannot simply square each term individually.