%5E2-as-a-trinomial-in-standard-form.jpeg "(x-8)^2 As A Trinomial In Standard Form")
Expanding (x-8)^2 into a Trinomial
The expression (x-8)^2 represents the square of the binomial (x-8). To expand it into a trinomial in standard form, we can use the following steps:
Understanding the Concept
The expression (x-8)^2 is equivalent to (x-8) multiplied by itself:
(x-8)^2 = (x-8) * (x-8)
Using the FOIL Method
To multiply the binomials, we can apply the FOIL method:
- First: Multiply the first terms of each binomial: x * x = x^2
- Outer: Multiply the outer terms of each binomial: x * -8 = -8x
- Inner: Multiply the inner terms of each binomial: -8 * x = -8x
- Last: Multiply the last terms of each binomial: -8 * -8 = 64
Combining Like Terms
Now, we add the resulting terms and combine like terms:
x^2 - 8x - 8x + 64 = x^2 - 16x + 64
Standard Form
Therefore, the trinomial in standard form is:
x^2 - 16x + 64
Key Points
- The standard form of a trinomial is ax^2 + bx + c, where a, b, and c are constants.
- FOIL method is a helpful tool for multiplying binomials.
We have successfully expanded (x-8)^2 into a trinomial in standard form.