(x+2)2 Foil Method

3 min read Jun 16, 2024

Understanding the FOIL Method with (x + 2)²

The FOIL method is a mnemonic acronym that helps us multiply two binomials. It stands for First, Outer, Inner, and Last, representing the order in which we multiply the terms. Let's break down how to apply this method to (x + 2)².

Expanding (x + 2)²

First: Multiply the first terms of each binomial: x * x = x²
Outer: Multiply the outer terms: x * 2 = 2x
Inner: Multiply the inner terms: 2 * x = 2x
Last: Multiply the last terms: 2 * 2 = 4

Now, we combine these results: x² + 2x + 2x + 4

Finally, simplify by combining like terms: x² + 4x + 4

Why Does the FOIL Method Work?

The FOIL method works because it ensures we multiply every term in the first binomial by every term in the second binomial. This is essential for obtaining the correct expanded form of the expression.

Applying the FOIL Method to Other Binomials

The FOIL method is applicable to any two binomials. Simply follow the same steps, substituting the specific terms of the binomials you are working with.

For example:

To expand (x - 3)(x + 5), follow the same steps:

First: x * x = x²
Outer: x * 5 = 5x
Inner: -3 * x = -3x
Last: -3 * 5 = -15

Combining and simplifying: x² + 5x - 3x - 15 = x² + 2x - 15

Beyond FOIL: Distributing Terms

The FOIL method is a specific case of the distributive property of multiplication. This property tells us that multiplying a sum by a number is equivalent to multiplying each term of the sum separately and then adding the results. You can think of FOIL as a systematic way to apply the distributive property to binomials.