(x-4).jpeg "(2x-5)(x-4)")
Expanding and Simplifying (2x-5)(x-4)
This article will guide you through the process of expanding and simplifying the expression (2x-5)(x-4).
Understanding the Process
The expression (2x-5)(x-4) represents the product of two binomials. To expand it, we need to apply the distributive property (also known as FOIL).
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.
Expanding the Expression
- First: Multiply the first terms of each binomial: 2x * x = 2x²
- Outer: Multiply the outer terms of the binomials: 2x * -4 = -8x
- Inner: Multiply the inner terms of the binomials: -5 * x = -5x
- Last: Multiply the last terms of each binomial: -5 * -4 = 20
Simplifying the Expression
Now we have: 2x² - 8x - 5x + 20
Combine the like terms (the terms with 'x'): 2x² - 13x + 20
Final Result
Therefore, the expanded and simplified form of (2x-5)(x-4) is 2x² - 13x + 20.
Conclusion
By applying the distributive property (FOIL) and simplifying the resulting expression, we were able to successfully expand and simplify the given binomial multiplication. This process is crucial in algebra and allows us to solve various equations and manipulate algebraic expressions.