(х-1)(х+1)(х-3)

To simplify the expression \((x-1)(x+1)(x-3)\), we can first multiply the first two factors:

\[ (x-1)(x+1) = x^2 - 1 \]

Now, we'll multiply this result by the third factor, \((x-3)\):

\[ (x^2 - 1)(x - 3) \]

Using the distributive property (also known as the FOIL method in this case), we can expand this product:

\[ = x^2(x - 3) - 1(x - 3) \]

Calculating each term:

1. \(x^2(x - 3) = x^3 - 3x^2\)
2. \(-1(x - 3) = -x + 3\)

Now, combine these results:

\[ x^3 - 3x^2 - x + 3 \]

Thus, the fully expanded form of the expression \((x-1)(x+1)(x-3)\) is:

\[ x^3 - 3x^2 - x + 3 \]