(2x-4).jpeg "(x-7)(2x-4)")
Expanding and Simplifying (x-7)(2x-4)
This article will guide you through the process of expanding and simplifying the expression (x-7)(2x-4).
Understanding the Concept
The expression (x-7)(2x-4) represents the product of two binomial expressions. To expand it, we need to use the distributive property (also known as FOIL method).
Expanding using FOIL
FOIL stands for First, Outer, Inner, Last:
- First: Multiply the first terms of each binomial: x * 2x = 2x²
- Outer: Multiply the outer terms of the binomials: x * -4 = -4x
- Inner: Multiply the inner terms of the binomials: -7 * 2x = -14x
- Last: Multiply the last terms of each binomial: -7 * -4 = 28
Combining these terms, we get: 2x² - 4x - 14x + 28
Simplifying the Expression
Finally, combine the like terms:
2x² - 18x + 28
Final Result
Therefore, the expanded and simplified form of (x-7)(2x-4) is 2x² - 18x + 28.