# Basic Algebra/Factoring/Squares of Binomials

## Contents

## Vocabulary[edit]

__Binomial__ - An algebraic expression with exactly two terms.

__Square__ - Multiply a number by itself.

__FOIL__ - The product of two binomials is the sum of the products of the **F**irst terms, the **O**uter terms, the **I**nner terms, and the **L**ast terms.

__Quantity__ -Total amount or number.

__Please note__ that the ‘FOIL’ method as well as the shortcut shown below is ONLY for binomial(s).

## Technical Equation[edit]

(a+b)^{2} = a^{2} + 2ab + b^{2}

(a-b)^{2} = a^{2} - 2ab + b^{2}

__NOTE__: These equations will work if you substitute the first term for **a** and the second term for **b**.
You may find these equations easier to understand after the concept is learned using the three steps described below.

## Lesson[edit]

Lesson 4 has shown you how to multiply binomials. In Lesson 5 we are going to learn how to square binomials. Squaring a binomial can be done using two different methods. The first method uses FOIL (refer to lesson 4). The second method is a shorter alternative to FOIL. The way we use the shortcut is to follow three simple steps.

__Step 1: __ Square the first term of the binomial.

__Step 2: __ Multiply the first term and last term of the binomial together and then double that quantity (in other words multiply by 2).

__Step 3: __ Square the last term of the binomial.

## Example Problems[edit]

**Here is an example to follow.**

Using the binomial (x_{T1}+6_{T2}) we will square it creating the problem (x+6)^{2}

__Step 1__ Square the first term of the binomial.

(x)^{2}=x^{2}

__Step 2__ Multiply the first term and last term of the binomial together and then double that quantity (in other words multiply by 2).

[(x)*(6)]*2 = (6x)*(2) = 12x

__Step 3__ Square the last term of the binomial.

(6)^{2} = 36

Finally we put the three term we have acquired together and get the answer

(x+6)^{2} = x^{2} + 12x + 36

**Let’s try another problem that may be a bit more difficult.**

Let’s square the binomial (x^{2}-4x) giving us (x^{2}-4x)^{2}

__Step 1__ Square the first term of the binomial.

(x^{2})^{2} = x^{4}

__Step 2__ Multiply the first term and last term of the binomial together and then double that quantity (in other words multiply by 2).

*Notice we keep the negative sign with the second term

[(x^{2})(-4x)]*2 = (-4x^{3})*(2) = -8x^{3}

__Step 3__ Square the last term of the binomial.

(-4x)^{2} = (-4)^{2}(x)^{2} = 16x^{2}

Our final answer will be the answers from the three steps combined

(x^{2}-4x)^{2} = x^{4} -8x^{3} + 16x^{2}

**Problem 3**
(2x-6y)^{2} = 4x^{2} - 24xy + 36y^{2}

## Online Lesson[edit]

You can use this link to view this lesson illustrated by a teacher.

http://www.phschool.com/atschool/academy123/html/bbapplet_wl-problem-431067.html

## Practice Problems[edit]

Use `^`

for exponentiation.