Select the expression that is equivalent to $$ (x-1)^{2} $$ $$ \begin{array}{l} ext { A. } x^{2}-2 x+2 \ ext { B. } x^{2}-x+2 \ ext { C. } x^{2}-2 x+1 \ ext { D. } x^{2}-x+1\end{array} $$

Question

Select the expression that is equivalent to $$ (x-1)^{2} $$ $$ \begin{array}{l}	ext { A. } x^{2}-2 x+2 \ 	ext { B. } x^{2}-x+2 \ 	ext { C. } x^{2}-2 x+1 \ 	ext { D. } x^{2}-x+1\end{array} $$

UpStudy AI · Accepted Answer

To find an expression equivalent to $$ (x-1)^{2} $$, let's expand the binomial:

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

Using the distributive property (also known as the FOIL method for binomials):

$$
= x \cdot x + x \cdot (-1) + (-1) \cdot x + (-1) \cdot (-1)
$$
$$
= x^2 - x - x + 1
$$
$$
= x^2 - 2x + 1
$$

So, the expanded form of $$ (x-1)^2 $$ is $$ x^2 - 2x + 1 $$.

**Answer:**  
**C.** $$ x^{2} - 2x + 1 $$
The equivalent expression is $$ x^{2} - 2x + 1 $$, which is choice C.

Select the expression that is equivalent to \( (x-1)^{2} \) \( \begin{array}{l}\text { A. } x^{2}-2 x+2 \\ \text { B. } x^{2}-x+2 \\ \text { C. } x^{2}-2 x+1 \\ \text { D. } x^{2}-x+1\end{array} \)

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