(x-4).jpeg "(x+8)(x-4)")
Expanding (x+8)(x-4)
This expression represents the product of two binomials: (x+8) and (x-4). To expand it, we can use the FOIL method:
First: Multiply the first terms of each binomial: x * x = x² Outer: Multiply the outer terms of the binomials: x * -4 = -4x Inner: Multiply the inner terms of the binomials: 8 * x = 8x Last: Multiply the last terms of each binomial: 8 * -4 = -32
Now, combine the terms:
x² - 4x + 8x - 32
Finally, simplify by combining the like terms:
x² + 4x - 32
Therefore, the expanded form of (x+8)(x-4) is x² + 4x - 32.
Understanding the FOIL Method
The FOIL method is a mnemonic device that helps remember the steps to multiply two 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 all possible combinations of terms from the two binomials are multiplied together.
Applications of Expanding Binomials
Expanding binomials is a fundamental skill in algebra. It is used in various contexts, including:
- Solving quadratic equations: Expanding binomials helps in factoring quadratic equations and finding their roots.
- Graphing quadratic functions: By expanding the equation, we can find the vertex, axis of symmetry, and other properties of the parabola.
- Simplifying expressions: Expanding binomials often simplifies complex expressions, making them easier to work with.
Understanding how to expand binomials is essential for success in algebra and other related fields.