%5E2-as-a-trinomial.jpeg "(x-5)^2 As A Trinomial")
Expanding (x-5)² as a Trinomial
In mathematics, we often encounter expressions that need to be expanded. One common example is squaring a binomial, like (x-5)². This expression represents the product of (x-5) multiplied by itself. Let's explore how to expand it into a trinomial.
Understanding the Concept
A trinomial is a polynomial with three terms. To expand (x-5)², we can use the FOIL method, which stands for First, Outer, Inner, Last.
FOIL Method:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms: x * -5 = -5x
- Inner: Multiply the inner terms: -5 * x = -5x
- Last: Multiply the last terms: -5 * -5 = 25
Now, combine all the terms: x² - 5x - 5x + 25
Simplifying the Expression
Finally, combine the like terms (-5x and -5x) to get the final trinomial:
x² - 10x + 25
Therefore, the expanded form of (x-5)² as a trinomial is x² - 10x + 25.
Summary
Expanding (x-5)² as a trinomial involves applying the FOIL method to multiply the binomial by itself. This process results in a trinomial with terms that can be simplified by combining like terms. The final trinomial is x² - 10x + 25.