%5E2-as-a-trinomial-in-standard-form.jpeg "(x-5)^2 As A Trinomial In Standard Form")
Expanding (x-5)^2 into a Trinomial in Standard Form
The expression (x-5)^2 represents the square of a binomial, which can be expanded into a trinomial in standard form. Here's how to do it:
Understanding the Concept
The expression (x-5)^2 means (x-5) multiplied by itself. Therefore, we can rewrite it as:
(x-5)^2 = (x-5)(x-5)
Expanding the Expression
To expand this product, we can use the FOIL method (First, Outer, Inner, Last):
- First: x * x = x^2
- Outer: x * -5 = -5x
- Inner: -5 * x = -5x
- Last: -5 * -5 = 25
Now, we add all the terms together:
x^2 - 5x - 5x + 25
Simplifying the Trinomial
Combining the like terms (-5x and -5x), we get:
x^2 - 10x + 25
Standard Form
The trinomial x^2 - 10x + 25 is now in standard form, where the terms are arranged in descending order of their exponents.
Therefore, the expansion of (x-5)^2 as a trinomial in standard form is x^2 - 10x + 25.