(2x-1).jpeg "(3x+1)(2x-1)")
Expanding the Expression (3x+1)(2x-1)
This article explores the expansion of the expression (3x+1)(2x-1), a common task in algebra.
The FOIL Method
We can expand this expression using the FOIL method, which stands for First, Outer, Inner, Last. This method helps us systematically multiply each term in the first binomial with each term in the second binomial.
1. First: Multiply the first terms of each binomial: (3x) * (2x) = 6x²
2. Outer: Multiply the outer terms of each binomial: (3x) * (-1) = -3x
3. Inner: Multiply the inner terms of each binomial: (1) * (2x) = 2x
4. Last: Multiply the last terms of each binomial: (1) * (-1) = -1
Combining Terms
Now, we combine the like terms we obtained: 6x² - 3x + 2x - 1
This simplifies to:
6x² - x - 1
Conclusion
Therefore, the expanded form of (3x+1)(2x-1) is 6x² - x - 1. This process demonstrates a fundamental skill in algebra: multiplying binomials using the FOIL method.