Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
Welcome to our Math lesson on Product of Conjugates, this is the fourth lesson of our suite of math lessons covering the topic of Special Algebraic Identities Obtained through Expanding, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Product of Conjugates
Two expressions of the form a + b and a - b are called the conjugates of each other. Basically, both are binomials that have the same terms but have opposite signs in-between.
Let's see what happens if we expand two conjugates that multiply with each other. Using the FOIL Rule, we obtain
(a - b)(a + b) = a ∙ a + a ∙ b - b ∙ a - b ∙ b
= a2 + ab - ab - b2
= a2 - b2
Example 3
The length of a square increased by 2 inches while the width decreased by 2 inches. How much did the area change? The area of square is calculated by the formula A = a2, where a is the side length of the square.
Solution 3
The new area is calculated by the formula
Anew = (a + 2) ∙ (a - 2)
= a2 - 22
= a2 - 4
When compared to the original area (Aold = a2), the new area is 4 units (square inches) smaller because
Aold - Anew = a2 - (a2 - 4)
= a2 - a2 + 4
= 4
More Special Algebraic Identities Obtained through Expanding Lessons and Learning Resources
Expressions Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 6.3 | Special Algebraic Identities Obtained through Expanding | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 6.3.1 | The Meaning of a Binomial | | |
| 6.3.2 | Square of a Sum | | |
| 6.3.3 | Square of a Difference | | |
| 6.3.4 | Product of Conjugates | | |
| 6.3.5 | Cube of a Sum | | |
| 6.3.6 | Cube of a Difference | | |
| 6.3.7 | Expanding the Algebraic Expression of the Form (a - b) · (a2 + ab + b2) | | |
| 6.3.8 | Expanding the Algebraic Expression of the Form (a + b) · (a2 - ab + b2) | | |
| 6.3.9 | Expanding Expressions of the Form (a + b + c)2 | | |
| 6.3.10 | Combining Special Identities | | |
Whats next?
Enjoy the "Product of Conjugates" math lesson? People who liked the "Special Algebraic Identities Obtained through Expanding lesson found the following resources useful:
- Product Of Conjugates Feedback. Helps other - Leave a rating for this product of conjugates (see below)
- Expressions Math tutorial: Special Algebraic Identities Obtained through Expanding. Read the Special Algebraic Identities Obtained through Expanding math tutorial and build your math knowledge of Expressions
- Expressions Video tutorial: Special Algebraic Identities Obtained through Expanding. Watch or listen to the Special Algebraic Identities Obtained through Expanding video tutorial, a useful way to help you revise when travelling to and from school/college
- Expressions Revision Notes: Special Algebraic Identities Obtained through Expanding. Print the notes so you can revise the key points covered in the math tutorial for Special Algebraic Identities Obtained through Expanding
- Expressions Practice Questions: Special Algebraic Identities Obtained through Expanding. Test and improve your knowledge of Special Algebraic Identities Obtained through Expanding with example questins and answers
- Check your calculations for Expressions questions with our excellent Expressions calculators which contain full equations and calculations clearly displayed line by line. See the Expressions Calculators by iCalculator™ below.
- Continuing learning expressions - read our next math tutorial: Factorising
Help others Learning Math just like you
Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
We hope you found this Math tutorial "Special Algebraic Identities Obtained through Expanding" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.
Expressions Calculators by iCalculator™