(2x%2B3).jpeg "(x-4)(2x+3)")
Expanding and Simplifying (x-4)(2x+3)
This article will walk through the process of expanding and simplifying the expression (x-4)(2x+3).
Understanding the Expression
The expression (x-4)(2x+3) represents the product of two binomials:
- (x-4) is a binomial with terms "x" and "-4"
- (2x+3) is a binomial with terms "2x" and "3"
Using the FOIL Method
The FOIL method is a common technique for expanding binomials. It stands for:
- First: Multiply the first terms of each binomial (x * 2x)
- Outer: Multiply the outer terms of the binomials (x * 3)
- Inner: Multiply the inner terms of the binomials (-4 * 2x)
- Last: Multiply the last terms of each binomial (-4 * 3)
Let's apply FOIL to our expression:
- First: x * 2x = 2x²
- Outer: x * 3 = 3x
- Inner: -4 * 2x = -8x
- Last: -4 * 3 = -12
Combining Like Terms
After applying FOIL, we get the following expression:
2x² + 3x - 8x - 12
Now, combine the like terms (3x and -8x):
2x² - 5x - 12
The Simplified Expression
Therefore, the expanded and simplified form of (x-4)(2x+3) is 2x² - 5x - 12.