FACTORING POLYNOMIALS BY DIFFERENCE OF TWO SQUARES | (Tagalog)
40This is a Module based lesson for MATH 8 with the topic FACTORING POLYNOMIALS BY DIFFERENCE OF TWO SQUARES for QUARTER 1 WEEK 1−2 : PART 2
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Lesson Flow:
0:14 Introduction
1:08 When to use Difference of Squares?
2:08 Formula for Difference of Two Squares
4:29 Expanding the factors
6:16 Example #1 Easy
8:19 Example #2 Easy
11:40 Example #3 Average
14:00 Example #4 Difficult
18:48 Example #5 Challenge
27:30 Closing message and References
You may also need to watch connected videos:
Common Monomials: https://youtu.be/kcc-hOlp6cM
Perfect Square Trinomials: https://youtu.be/aI_9wzkm_f4
General Trinomials: https://youtu.be/fl0Z6x7hN2E
In this video, we are going to discuss about factoring difference of two squares. We will have some simple problems at first so that we can discuss the steps carefully one by one then as we progress, we will have a much more challenging problems so make sure to watch until the end of the video.
The difference of two squares is one of the most common. The good news is this form is very easy to identify. Whenever you have a binomial with each term being squared (having an exponent of 2), and they have subtraction as the middle sign, you are guaranteed to have the case of difference of two squares.
For, the like terms will cancel.
Symmetrically, the difference of two squares can be factored:
x2 − 25 = (x + 5)(x − 5)
x2 is the square of x. 25 is the square of 5.
The first term of the binomial is definitely a perfect square because the variable x is being raised to the second power. However, the second term of the binomial is not written as a square. So we need to rewrite it in such a way that 99 is expressed as some number with a power of 2. I hope you can see that 9 = 3 to the power of 2. Clearly, we have a difference of two squares because the sign between the two squared terms is subtraction.
At first, it appears that this is not a difference of two squares. What we need is to try rewriting it in the form that is easily recognizable. For the first term of the binomial, what term when multiplied by itself
This problem is a little bit different because both terms of the binomial contain variables. If we can show that they are perfect squares then we should be alright!
Here’s an interesting problem. Maybe you already recognize that the pure numbers, 16 and 81, are perfect squares. That’s good. The variable y though doesn’t have an exponent of 2, but instead has an exponent of 4. Does this qualify to be a square? Don’t be quick to conclude that it is not. Can you think of a term which when multiplied by itself gives {y^4}? You can do a trial and error on this. But if you apply your previous knowledge of the Product Rule of Exponents, it makes sense that
References:
https://www.chilimath.com/lessons/intermediate-algebra/factoring-difference-of-two-squares/
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