(x-11)^2 As A Trinomial In Standard Form

Jasonbradley

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Jun 17, 2024

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Expanding (x-11)^2 into a Trinomial in Standard Form

The expression (x-11)^2 represents the square of a binomial. To expand it into a trinomial in standard form, we can use the FOIL method or the pattern for squaring a binomial.

Using FOIL Method

First: x * x = x^2 Outer: x * -11 = -11x Inner: -11 * x = -11x Last: -11 * -11 = 121

Adding all the terms together, we get:

x^2 - 11x - 11x + 121

Combining like terms, the final trinomial in standard form is:

x^2 - 22x + 121

Using the Pattern for Squaring a Binomial

The pattern for squaring a binomial is:

(a - b)^2 = a^2 - 2ab + b^2

In our case, a = x and b = 11.

Substituting these values into the pattern, we get:

x^2 - 2(x)(11) + 11^2

Simplifying the expression gives us:

x^2 - 22x + 121

Both methods yield the same result, confirming that (x-11)^2 expanded as a trinomial in standard form is x^2 - 22x + 121.