(3x-4).jpeg "(2x-5)(3x-4)")
Expanding the Expression: (2x - 5)(3x - 4)
In algebra, we often encounter expressions that involve multiplying binomials. One such example is (2x - 5)(3x - 4). To simplify this expression, we need to expand it using the distributive property (also known as FOIL).
Understanding the FOIL Method
FOIL 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:
- First: Multiply the first terms of each binomial: (2x)(3x) = 6x²
- Outer: Multiply the outer terms of the binomials: (2x)(-4) = -8x
- Inner: Multiply the inner terms of the binomials: (-5)(3x) = -15x
- Last: Multiply the last terms of each binomial: (-5)(-4) = 20
Combining the Terms
Now, we have four terms: 6x², -8x, -15x, and 20. Combining the like terms (-8x and -15x), we get:
6x² - 8x - 15x + 20
Finally, simplifying the expression, we get:
6x² - 23x + 20
Conclusion
Therefore, the expanded form of the expression (2x - 5)(3x - 4) is 6x² - 23x + 20. Understanding the FOIL method is crucial for simplifying algebraic expressions and solving equations involving binomials.