(x+6)(x-1)

Jasonbradley

2 min read

·

Jun 17, 2024

10

Share

Expanding and Simplifying (x+6)(x-1)

This expression represents the product of two binomials: (x+6) and (x-1). To simplify it, we need to expand it using the distributive property, also known as FOIL.

FOIL 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.

Let's apply this to our expression:

F: x * x = x² O: x * -1 = -x I: 6 * x = 6x L: 6 * -1 = -6

Now, we combine all the terms:

x² - x + 6x - 6

Finally, we simplify by combining like terms:

x² + 5x - 6

Therefore, the simplified form of (x+6)(x-1) is x² + 5x - 6.

Understanding the Result

This expanded form represents a quadratic equation. It can be graphed as a parabola, and its roots (where the graph intersects the x-axis) can be found by setting the equation equal to zero and solving for x.

Key Points:

• FOIL is a useful tool for expanding products of binomials.
• The simplified expression represents a quadratic equation.
• The result can be used for further algebraic manipulation and problem solving.