Quadratic Factoring B5D620

1. **State the problem:** Simplify or factor the quadratic expression $$X^2 + 9x - 400$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look for two numbers that multiply to $$a \times c$$ and add to $$b$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = 9$$, and $$c = -400$$. 4. **Calculate product:** $$a \times c = 1 \times (-400) = -400$$. 5. **Find two numbers:** We need two numbers that multiply to $$-400$$ and add to $$9$$. These numbers are $$25$$ and $$-16$$ because $$25 \times (-16) = -400$$ and $$25 + (-16) = 9$$. 6. **Rewrite the middle term:** $$X^2 + 25x - 16x - 400$$. 7. **Group terms:** $$(X^2 + 25x) + (-16x - 400)$$. 8. **Factor each group:** $$X(X + 25) - 16(X + 25)$$. 9. **Factor out common binomial:** $$(X - 16)(X + 25)$$. 10. **Final answer:** The factored form of $$X^2 + 9x - 400$$ is $$(X - 16)(X + 25)$$.