Basic Algebra/Factoring/Squares of Binomials

Vocabulary

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 dio of the First terms, the Outer terms, the Inner terms, and the Last 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

(a+b)² = a² + 2ab + b²

(a-b)² = a² - 2ab + b²

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

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

Here is an example to follow.

Using the binomial x²+12x+36 we will square it creating the problem (x+6)²

Step 1 Square the first term of the binomial.

(x)²=x²

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 = x² + 12x + 36

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

Let’s square the binomial (x²-4x) giving us (x²-4x)²

Step 1 Square the first term of the binomial.

(x²)² = x⁴

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

[(x²)(-4x)]*2 = (-4x³)*(2) = -8x³

Step 3 Square the last term of the binomial.

(-4x)² = (-4)²(x)² = 16x²

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

(x²-4x)² = x⁴ -8x³ + 16x²

Problem 3 (2x-6y)² = 4x² - 24xy + 36y²

Online Lesson

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

Use ^ for exponentiation.