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