%5E2-as-a-trinomial-in-standard-form.jpeg "(x-12)^2 As A Trinomial In Standard Form")
Expanding (x - 12)² as a Trinomial
The expression (x - 12)² represents the square of a binomial. To expand this expression and write it in standard form as a trinomial, we can use the FOIL method or the square of a binomial formula.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -12 = -12x
- Inner: Multiply the inner terms of the binomials: -12 * x = -12x
- Last: Multiply the last terms of each binomial: -12 * -12 = 144
Now, combine the like terms:
x² - 12x - 12x + 144 = x² - 24x + 144
Using the Square of a Binomial Formula
The formula for squaring a binomial is:
(a - b)² = a² - 2ab + b²
In our case, a = x and b = 12. Substituting these values into the formula:
x² - 2(x)(12) + 12² = x² - 24x + 144
The Result
Therefore, the expanded form of (x - 12)² in standard form as a trinomial is x² - 24x + 144.