(x-4)-foil.jpeg "(4x-4)(x-4) Foil")
Multiplying Binomials: (4x - 4)(x - 4) using FOIL
The FOIL method is a mnemonic acronym that stands for First, Outer, Inner, Last. It's a helpful way to remember the steps to multiply two binomials.
Let's break down how to use FOIL to multiply (4x - 4)(x - 4):
1. First: Multiply the first terms of each binomial.
(4x - 4)(x - 4) = **4x * x** = 4x²
2. Outer: Multiply the outer terms of the binomials.
(4x - 4)(x - 4) = 4x * **-4** = -16x
3. Inner: Multiply the inner terms of the binomials.
(4x - 4)(x - 4) = **-4 * x** = -4x
4. Last: Multiply the last terms of the binomials.
(4x - 4)(x - 4) = **-4 * -4** = 16
5. Combine Like Terms: Add the results of steps 1-4:
4x² - 16x - 4x + 16 = **4x² - 20x + 16**
Therefore, (4x - 4)(x - 4) = 4x² - 20x + 16
Key Points
- FOIL is a great method for remembering to multiply all possible combinations of terms in two binomials.
- Always combine like terms after applying FOIL to simplify the final expression.
Practice Tip
Use FOIL to multiply other binomial expressions. You can also check your answers by using the distributive property to multiply the binomials.