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

Quantity -Total amount or number.

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. I 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 (x+6) 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 one more problem that may be a 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

Online Lesson

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

(2x-6y)2 = 2x2 - 6xy + 6y2