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.