(3x-1).jpeg "(2x-1)(3x-1)")
Expanding the Expression (2x-1)(3x-1)
The expression (2x-1)(3x-1) represents the product of two binomials. To expand this, we can use the FOIL method, which 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.
Let's apply this to our expression:
1. First: (2x) * (3x) = 6x²
2. Outer: (2x) * (-1) = -2x
3. Inner: (-1) * (3x) = -3x
4. Last: (-1) * (-1) = 1
Now, we combine all the terms:
6x² - 2x - 3x + 1
Finally, we simplify by combining the like terms:
6x² - 5x + 1
Therefore, the expanded form of (2x-1)(3x-1) is 6x² - 5x + 1.
Further Applications
This expanded form can be used in various mathematical contexts, such as:
- Solving equations: We can set the expression equal to zero and solve for the value of x.
- Finding the roots: The roots of the equation 6x² - 5x + 1 = 0 represent the x-values where the expression equals zero.
- Graphing the function: The expanded form helps in plotting the graph of the function y = 6x² - 5x + 1.
Understanding the expansion of binomial expressions is a fundamental skill in algebra, essential for solving equations, graphing functions, and other related applications.