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Welcome to our Math lesson on Square of a Difference, this is the third 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.
Square of a Difference
The square of a difference involves algebraic expressions of the type
(a - b)2
that are very similar to those discussed in the previous paragraph. The only difference is the negative sign preceding the second term. Again, we use the FOIL method to expand this expression (we must also follow the sign rules). Thus,
(a - b)2 = (a - b) ∙ (a - b)
= a ∙ a + a ∙ (-b) - b ∙ a - b ∙ (-b)
= a2 - ab - ab + b2
= a2 - 2ab + b2
The last expression represents the right part of the second special algebraic identity
(a - b)2 = a2 - 2ab + b2
which tells us how to expand the square of a difference.
Example 2
Calculate the difference of two unknown numbers x and y (x > y) if x2 + y2 = 19 and x · y = 5.
Solution 2
We use the formula of the square of a difference to solve this exercise. Giving that
x ∙ y = 5
we obtain
2 ∙ x ∙ y = 2 ∙ 5 = 10
Thus, since
x2 + y2 = 19
and
x2 + y2 - 2xy = x2 - 2xy + y2= 19 - 10= 9
we obtain
(x - y)2 = x2 - 2xy + y2 = 9
Thus, x - y = 3 because (x - y)2 = 32 = 9.
More Special Algebraic Identities Obtained through Expanding Lessons and Learning Resources
Expressions Learning MaterialTutorial ID | Math Tutorial Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions |
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6.3 | Special Algebraic Identities Obtained through Expanding | | | | |
Lesson ID | Math Lesson Title | Lesson | Video Lesson |
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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 | | |
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- Continuing learning expressions - read our next math tutorial: Factorising
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