(x-6).jpeg "(x+2)(x-6)")
Expanding the Expression: (x+2)(x-6)
This article will explore the expansion of the expression (x+2)(x-6). This type of expression represents a product of two binomials, and expanding it involves using the distributive property (also known as FOIL).
Understanding the FOIL Method
FOIL stands for First, Outer, Inner, Last. It is a mnemonic device used to remember the steps for multiplying two binomials:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Expanding the Expression
Let's apply FOIL to our expression (x+2)(x-6):
- First: x * x = x²
- Outer: x * -6 = -6x
- Inner: 2 * x = 2x
- Last: 2 * -6 = -12
Now we combine the results:
x² - 6x + 2x - 12
Finally, we simplify by combining like terms:
x² - 4x - 12
Conclusion
Therefore, the expanded form of the expression (x+2)(x-6) is x² - 4x - 12. Expanding binomials is a fundamental skill in algebra, and understanding the FOIL method makes this process straightforward.