Jasonbradley
Home

(x+4)(x−1)

3 min read Jun 16, 2024
(x+4)(x−1)

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:

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

Featured Posts