%5E2.jpeg "(4x-5)^2")
Expanding the Square: (4x - 5)^2
In algebra, we often encounter expressions that need to be simplified or expanded. One common type is the square of a binomial, such as (4x - 5)^2. Let's break down how to expand this expression.
Understanding the Square of a Binomial
The square of a binomial means multiplying the binomial by itself. In this case, we have:
(4x - 5)^2 = (4x - 5) * (4x - 5)
Using the FOIL Method
To expand the expression, we can utilize the FOIL method (First, Outer, Inner, Last).
- First: Multiply the first terms of each binomial: (4x) * (4x) = 16x^2
- Outer: Multiply the outer terms: (4x) * (-5) = -20x
- Inner: Multiply the inner terms: (-5) * (4x) = -20x
- Last: Multiply the last terms: (-5) * (-5) = 25
Combining Like Terms
Now, combine the terms obtained from the FOIL method:
16x^2 - 20x - 20x + 25 = 16x^2 - 40x + 25
Final Result
Therefore, the expanded form of (4x - 5)^2 is 16x^2 - 40x + 25.
Key Points
- FOIL method: A handy technique for expanding binomials.
- Combine like terms: Ensure the final expression is simplified.
- Practice: Expanding squares of binomials is a fundamental skill in algebra.