(2x-1).jpeg "(2x-5)(2x-1)")
Expanding the Expression (2x-5)(2x-1)
This article will guide you through the process of expanding the expression (2x-5)(2x-1) using the FOIL method.
Understanding the FOIL Method
The FOIL method is a mnemonic device used to remember the steps in multiplying two binomials. It stands for:
- 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.
Applying the FOIL Method to (2x-5)(2x-1)
- First: (2x) * (2x) = 4x²
- Outer: (2x) * (-1) = -2x
- Inner: (-5) * (2x) = -10x
- Last: (-5) * (-1) = 5
Now, combine all the terms: 4x² - 2x - 10x + 5
Simplifying the Expression
Finally, combine the like terms: 4x² - 12x + 5
Therefore, the expanded form of (2x-5)(2x-1) is 4x² - 12x + 5.
Conclusion
By using the FOIL method, we successfully expanded the expression (2x-5)(2x-1) into its simplified form, 4x² - 12x + 5. This method provides a structured approach to multiplying binomials, ensuring that all terms are accounted for and the expression is simplified correctly.