## Solving Quadratic Equations: From Factored Form to Standard Form

This article focuses on understanding the relationship between **factored form** and **standard form** of a quadratic equation, specifically using the example: **(x + 4)(x - 5) = 0**.

### Understanding Factored Form

The equation **(x + 4)(x - 5) = 0** is presented in factored form. This form is useful for quickly finding the **roots** or **solutions** of the equation.

**The Zero Product Property** states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying this to our equation:

**x + 4 = 0**or**x - 5 = 0**- Solving for x in each case, we get:
**x = -4****x = 5**

Therefore, the roots of the equation **(x + 4)(x - 5) = 0** are **x = -4** and **x = 5**.

### Converting to Standard Form

The standard form of a quadratic equation is **ax² + bx + c = 0**, where a, b, and c are constants and a ≠ 0.

To convert our factored form into standard form, we need to expand the product:

**FOIL Method:**We multiply each term in the first factor by each term in the second factor.**(x + 4)(x - 5) = x(x - 5) + 4(x - 5)**

**Simplify:**We distribute and combine like terms.**x² - 5x + 4x - 20 = 0**

**Combine Like Terms:****x² - x - 20 = 0**

Therefore, the standard form of the quadratic equation **(x + 4)(x - 5) = 0** is **x² - x - 20 = 0**.

### Conclusion

By understanding the relationship between factored form and standard form, we can efficiently solve quadratic equations. The factored form provides a direct path to finding the roots, while the standard form is essential for various mathematical operations and applications.