1. Lesson 6

1.6. Explore 2

Mathematics 20-2 M3 Lesson 6

Module 3: Quadratics

 

Difference of Squares
 

Some factoring questions will only have two terms. The process used to factor in such cases is called factoring by a difference of squares. To factor by a difference of squares, a question must have two terms and a subtraction sign between the terms, and each term must be a perfect square.

 

Watch Factoring a Difference of Squares to learn more.

 

 

This is a play button that opens Factoring a Difference of Squares.

 

Self-Check 4
 

Factor the following binomials.

  1. x2 − 64 Answer

  2. y2 − 81 Answer

  3. −3x2 + 27 Answer

  4. 4y2 − 4 Answer

caution

You have practised your factoring skills in preparation for solving quadratic equations. The factoring questions you have been working on can be changed into quadratic equations by making the questions equal to 0.

 

For example, if you were asked to factor x2 + x − 20, you would get the answer (x + 5)(x − 4). If you were asked to solve x2 + x − 20 = 0, you would get (x + 5)(x − 4) = 0 and then proceed to the roots x = −5 and x = +4. The sign will always be reversed because x + 5 = 0 only when x = −5 and x − 4 = 0 only when x = +4.

 

If there is a factor like (2x − 3), you can start by setting the factor equal to 0.

 

 

2x − 3 = 0

 

The variable needs to be isolated, so the 3 needs to be moved to the other side.

 

 

2x = 3

 

Then divide by 2 to get m3_eqn016.eps

 

This is a rational root, since it is a rational number.


glossary

Recall from the Course Introduction that you will be creating your own course glossary. Open the Glossary Terms document that you saved to your course folder, and add in any new terms. You might choose to add the following terms to your copy of Glossary Terms:

  • perfect square
  • rational root
  • integral root