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(2x+4)(x-4)

3 min read Jun 16, 2024
(2x+4)(x-4)

Expanding the Expression (2x + 4)(x - 4)

This expression represents the product of two binomials: (2x + 4) and (x - 4). To simplify it, we can use the FOIL method:

First: Multiply the first terms of each binomial: 2x * x = 2x²

Outer: Multiply the outer terms of the binomials: 2x * -4 = -8x

Inner: Multiply the inner terms of the binomials: 4 * x = 4x

Last: Multiply the last terms of each binomial: 4 * -4 = -16

Now, add all the terms together:

2x² - 8x + 4x - 16

Combine the like terms:

2x² - 4x - 16

Therefore, the expanded form of (2x + 4)(x - 4) is 2x² - 4x - 16.

Understanding the FOIL Method

The FOIL method is a mnemonic device that helps remember the steps for multiplying binomials. It stands for:

  • First: Multiply the first terms of each binomial.
  • Outer: Multiply the outer terms of the binomials.
  • Inner: Multiply the inner terms of the binomials.
  • Last: Multiply the last terms of each binomial.

This method ensures that you multiply every term in the first binomial by every term in the second binomial.

Applications of Expanding Binomials

Expanding binomials is a fundamental skill in algebra and has many applications, including:

  • Factoring quadratic expressions: The expanded form of a binomial product can help in factoring quadratic expressions.
  • Solving quadratic equations: Expanding binomials can be used to rewrite quadratic equations in standard form and solve for the unknown variable.
  • Graphing quadratic functions: The expanded form can help determine the vertex, intercepts, and other properties of the graph.
  • Calculus: Expanding binomials is essential for differentiating and integrating functions.

Expanding binomials is a crucial skill that forms the foundation for more advanced algebraic concepts. By understanding the FOIL method and its applications, you can confidently work with algebraic expressions and solve various problems.

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