Express (x-1)^2
as a trinomial in standard form.

Final answer:

To express (x-1)^2 as a trinomial in standard form, we expand the square using the formula (a-b)^2 = a^2 - 2ab + b^2. Substituting a = x and b = 1, we get x^2 - 2x + 1.

Explanation:

To express the expression (x-1)^2 as a trinomial in standard form, we need to apply the square of a binomial formula, which is (a - b)^2 = a^2 - 2ab + b^2. In this case, a is x, and b is 1. Substituting these values into the formula, we get:

(x - 1)^2 = x^2 - 2(x)(1) + 1^2

Now, simplify each term:

1. x^2 represents the square of the first term, which is x.

2. 2(x)(1) = 2x, representing twice the product of x and 1.

3. 1^2 = 1, which is the square of the second term, 1.

So, when we simplify the expression further, we have:

(x - 1)^2 = x^2 - 2x + 1

This is the trinomial representation of (x-1)^2 in standard form. It consists of three terms: x^2, -2x, and 1, with each term having a specific coefficient.

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Answer:

x² - 2x + 1

Step-by-step explanation:

We want to express (x - 1)² as a trinomial. In other words, we want to expand this out.

(x - 1)² = (x - 1)(x - 1)

We use FOIL (First, Outer, Inner, Last). The First terms are x and x. Multiply:

x * x = x²

The outer terms are x and -1. Multiply:

x * (-1) = -x

The inner terms are -1 and x; multiply:

(-1) * x = -x

The last terms are -1 and -1; multiply:

(-1) * (-1) = 1

Add all these together:

x² + (-x) + (-x) + 1 = x² - 2x + 1

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