(x-1)(x+5)

Jasonbradley

3 min read

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Jun 17, 2024

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Expanding and Simplifying (x-1)(x+5)

This expression represents the product of two binomials: (x-1) and (x+5). To simplify it, 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 the binomials: x * 5 = 5x
3. Inner: Multiply the inner terms of the binomials: -1 * x = -x
4. Last: Multiply the last terms of each binomial: -1 * 5 = -5

Now, combine all the terms:

x² + 5x - x - 5

Finally, simplify by combining like terms:

x² + 4x - 5

Therefore, the simplified form of (x-1)(x+5) is x² + 4x - 5.

What does this represent?

The simplified expression, x² + 4x - 5, is a quadratic equation. It represents a parabola when graphed, and its solutions (or roots) are the x-values where the parabola intersects the x-axis. These roots can be found using methods like factoring, completing the square, or the quadratic formula.

Applications

Understanding how to expand and simplify expressions like (x-1)(x+5) is crucial in various areas of mathematics, including:

• Algebra: Solving equations, inequalities, and working with polynomial expressions.
• Calculus: Finding derivatives and integrals, and analyzing functions.
• Physics: Modeling physical phenomena like projectile motion or the behavior of springs.
• Engineering: Designing structures, circuits, and systems.

By mastering this fundamental skill, you'll be well-equipped to tackle more complex mathematical problems across various disciplines.