(3x-1).jpeg "(2x+5)(3x-1)")
Expanding the Expression: (2x+5)(3x-1)
This article explores the process of expanding the algebraic expression (2x+5)(3x-1). We'll delve into the concept of FOIL and its application in simplifying such expressions.
Understanding the FOIL Method
FOIL is an acronym that stands for First, Outer, Inner, Last. It's a simple yet effective technique for multiplying two binomials. Let's break down each step:
- First: Multiply the first terms of each binomial: (2x) * (3x) = 6x²
- Outer: Multiply the outer terms of the binomials: (2x) * (-1) = -2x
- Inner: Multiply the inner terms of the binomials: (5) * (3x) = 15x
- Last: Multiply the last terms of each binomial: (5) * (-1) = -5
Combining Like Terms
Now that we've expanded the expression, we can combine the like terms:
6x² - 2x + 15x - 5 = 6x² + 13x - 5
Conclusion
By applying the FOIL method, we successfully expanded the expression (2x+5)(3x-1) and simplified it to 6x² + 13x - 5. This technique provides a structured approach for multiplying binomials and simplifying the resulting expressions.