1. **State the problem:** Simplify or factor the expression $x^2 - xy - 2y^2$. 2. **Recall the factoring formula:** For a quadratic expression in two variables, $ax^2 + bxy + cy^2$, we look for two binomials $(x + py)(x + qy)$ such that $pq = c$ and $p + q = b$. 3. **Identify coefficients:** Here, $a=1$, $b=-1$, and $c=-2$. 4. **Find factors of $c=-2$ that add to $b=-1$:** The pairs are $(1, -2)$ and $(-1, 2)$. The pair $1$ and $-2$ sums to $-1$. 5. **Write the factorization:** $$x^2 - xy - 2y^2 = (x + y)(x - 2y)$$ 6. **Explanation:** We split the middle term $-xy$ into $+y imes x$ and $-2y imes x$ to factor by grouping. **Final answer:** $$x^2 - xy - 2y^2 = (x + y)(x - 2y)$$