## Expanding the Expression (x+4)(x-1)

The expression (x+4)(x-1) represents the product of two binomials. To expand this expression, we can use the **FOIL** method, which stands for **First, Outer, Inner, Last**.

Here's how it works:

**First:**Multiply the**first**terms of each binomial: x * x = x²**Outer:**Multiply the**outer**terms of each binomial: x * -1 = -x**Inner:**Multiply the**inner**terms of each binomial: 4 * x = 4x**Last:**Multiply the**last**terms of each binomial: 4 * -1 = -4

Now, we have the following terms: x², -x, 4x, and -4. Combine the like terms (-x and 4x) to get the final expanded form:

**(x+4)(x-1) = x² + 3x - 4**

## Understanding the Result

The expanded expression x² + 3x - 4 is a **quadratic equation**, which is a polynomial of degree 2. This equation can be used to represent various situations in mathematics and other fields, such as calculating areas, modeling projectile motion, or analyzing financial data.

## Applications

Understanding how to expand binomials like (x+4)(x-1) is crucial in algebra and other areas of mathematics. Some applications include:

**Solving quadratic equations:**Expanding and simplifying the expression helps in finding the roots or solutions of the equation.**Factoring polynomials:**Recognizing the pattern in the expanded expression allows us to factor it back into its original binomial form.**Graphing quadratic functions:**The expanded form helps determine the shape and key features of the graph of the function.**Modeling real-world scenarios:**Quadratic equations can be used to model various real-world situations, such as the trajectory of a ball thrown in the air or the growth of a population.

By understanding the process of expanding binomials like (x+4)(x-1), you gain a fundamental tool for solving various mathematical problems and applying them to real-world situations.