(x-4).jpeg "(2x+1)(x-4)")
Expanding the Expression (2x+1)(x-4)
This article will demonstrate how to expand the algebraic expression (2x+1)(x-4) and discuss the resulting quadratic equation.
The FOIL Method
The most common method for expanding this expression is FOIL, which stands for First, Outer, Inner, Last. This method ensures that every term in the first binomial is multiplied by every term in the second binomial.
1. First: Multiply the first terms of each binomial: (2x) * (x) = 2x² 2. Outer: Multiply the outer terms of the binomials: (2x) * (-4) = -8x 3. Inner: Multiply the inner terms of the binomials: (1) * (x) = x 4. Last: Multiply the last terms of each binomial: (1) * (-4) = -4
Combining Like Terms
Now, we combine the like terms in the expanded expression:
2x² - 8x + x - 4 = 2x² - 7x - 4
Conclusion
Therefore, the expanded form of (2x+1)(x-4) is 2x² - 7x - 4. This is a quadratic equation, which is characterized by its highest power being 2.
Further Exploration
- This quadratic equation can be further analyzed by finding its roots (the x-values where the equation equals zero) using factoring, completing the square, or the quadratic formula.
- The equation can be graphed to visualize its shape and intercept points.
- Understanding how to expand expressions like this is crucial for solving algebraic equations and manipulating polynomials in more complex scenarios.