To simplify the expression \((x-3)(x+1)\), you can use the distributive property (also known as the FOIL method for binomials):
\[ (x-3)(x+1) = x \cdot x + x \cdot 1 - 3 \cdot x - 3 \cdot 1 \]
Now, perform the multiplication:
\[ = x^2 + x - 3x - 3 \]
Next, combine like terms:
\[ = x^2 - 2x - 3 \]
So, the simplified form of \((x-3)(x+1)\) is:
\[ x^2 - 2x - 3 \]