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

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Final answer:

The binomial (x-1)² can be expressed as the trinomial x² - 2x + 1 by expanding the square using the distributive property or the formula (a-b)² = a² - 2ab + b².

Step-by-step explanation:

To express the binomial (x-1)² as a trinomial in standard form, we need to expand the square. This involves applying the distributive property or using the formula (a-b)² = a² - 2ab + b². For the expression (x-1)², the steps are as follows:

1. Identify a and b in the expression, such that a = x and b = 1.

2. Calculate a², which is x².

3. Calculate 2ab, which is 2*x*1 or 2x.

4. Calculate b², which is 1² or 1.

5. Combine these results into the trinomial form: a² - 2ab + b².

The final expanded form is x² - 2x + 1.

User Paolo Bonzini
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