(x+1)(x+1) Foil

3 min read Jun 16, 2024

FOIL Method: A Step-by-Step Guide to Expanding (x+1)(x+1)

The FOIL method is a helpful technique for expanding binomials, which are expressions with two terms. It's an acronym that stands for First, Outer, Inner, Last. Let's break down how to use FOIL to expand (x+1)(x+1).

Understanding FOIL

First: Multiply the first terms of each binomial: x * x = x²
Outer: Multiply the outer terms of the binomials: x * 1 = x
Inner: Multiply the inner terms of the binomials: 1 * x = x
Last: Multiply the last terms of each binomial: 1 * 1 = 1

Combining the Terms

Now, we have four terms: x², x, x, and 1. Combine the like terms:

x² + x + x + 1 = x² + 2x + 1

The Final Result

Therefore, the expanded form of (x+1)(x+1) using the FOIL method is x² + 2x + 1.

Why FOIL Works

The FOIL method is essentially a visual representation of the distributive property. When we expand (x+1)(x+1), we are essentially multiplying each term in the first binomial by each term in the second binomial.

Here's how it looks:

(x + 1)(x + 1) = x(x + 1) + 1(x + 1)

Using the distributive property, we get:

x² + x + x + 1

This is the same result we obtained using the FOIL method!

In Summary

The FOIL method is a simple and efficient way to expand binomials. By following the First, Outer, Inner, Last steps, you can systematically multiply the terms and obtain the correct expanded form. Remember, understanding the underlying distributive property gives you a deeper understanding of how FOIL works.