Factoring 16 Sum of 2 squares is prime
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Meets NCTM Standards:
Lesson Summary:
In this lesson, students learn why the belief that two perfect squares added together can be factored is incorrect. By providing a clear example, the instructor demonstrates that factoring a squared plus b squared is not possible. However, the instructor points out that the difference of two squares can be factored, as shown in a numerical example. Ultimately, this lesson emphasizes the importance of understanding the difference between these two concepts in order to correctly factor polynomials.
Lesson Description:
Emphasizes that the sum of two perfect squares usually is nonfactorable and is prime.
More free YouTube videos by Julie Harland are organized at http://yourmathgal.com
Questions answered by this video:
- Why can you not factor the sum of squares?
- Why does (a + b)^2 NOT equal a^2 + b^2?
- What does (a + b)^2 equal?
- Why can you not factor a^2 + b^2?
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Staff Review
This lesson breaks a common student misconception -- that squaring the sum of two terms is the same as the sum of each term squared. Or in other words, that (a + b)^2 equals a^2 + b^2. This video explains why that is not the case, and therefore, why a^2 + b^2 cannot be factored.
