%5E2-as-a-trinomial-in-standard-form.jpeg "(x-1)^2 As A Trinomial In Standard Form")
Expanding (x - 1)^2 into a Trinomial
The expression (x - 1)^2 represents the square of the binomial (x - 1). To express it as a trinomial in standard form, we need to expand it using the distributive property or the FOIL method.
Using the Distributive Property
The distributive property states that a(b + c) = ab + ac. Applying this to our problem, we have:
(x - 1)^2 = (x - 1)(x - 1)
Expanding using the distributive property:
- Step 1: x * (x - 1) = x^2 - x
- Step 2: -1 * (x - 1) = -x + 1
Now, we combine the results:
x^2 - x - x + 1
Finally, we combine like terms to get the trinomial in standard form:
x^2 - 2x + 1
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. It's a mnemonic device to remember the order of multiplying terms in two binomials.
- First: x * x = x^2
- Outer: x * -1 = -x
- Inner: -1 * x = -x
- Last: -1 * -1 = 1
Combining these terms, we get:
x^2 - x - x + 1
Again, combining like terms gives us:
x^2 - 2x + 1
Therefore, (x - 1)^2 expressed as a trinomial in standard form is x^2 - 2x + 1.