1. **State the problem:** We are given the equation $(x + 2)(x - 5) = x^2 - 2x - 15$ and need to verify if both sides are equal by expanding and simplifying. 2. **Recall the formula:** To expand the product of two binomials, use the distributive property (FOIL method): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Expand the left side:** $$ (x + 2)(x - 5) = x \cdot x + x \cdot (-5) + 2 \cdot x + 2 \cdot (-5) = x^2 - 5x + 2x - 10 $$ 4. **Simplify the left side:** $$ x^2 - 5x + 2x - 10 = x^2 - 3x - 10 $$ 5. **Compare with the right side:** The right side is given as: $$ x^2 - 2x - 15 $$ 6. **Conclusion:** Since $$ x^2 - 3x - 10 \neq x^2 - 2x - 15 $$ the original equation is not true as stated. The left side simplifies to $x^2 - 3x - 10$, which is different from the right side $x^2 - 2x - 15$. **Final answer:** The equation $(x + 2)(x - 5) = x^2 - 2x - 15$ is false because the expanded left side is $x^2 - 3x - 10$, not $x^2 - 2x - 15$.