1. **State the problem:** Simplify the expression $x \times x - x \times 2$. 2. **Recall the rules:** Multiplication is associative and distributive over subtraction. 3. **Rewrite the expression:** $x \times x - x \times 2 = x^2 - 2x$ 4. **Factor the expression:** Factor out the common term $x$: $$x^2 - 2x = x(x - 2)$$ 5. **Final answer:** The simplified and factored form is: $$x(x - 2)$$