Showing posts with label Algebra. Show all posts
Visual and Geometric Proof of Algebraic Identities
There are a lot of algebraic identities. One of the most commonly used identity is the identity
(a+b)^2 = a^2 + 2ab + b^2.
Did you ever wondered where did it came from?
There are various ways on how to prove this algebraic identity. One of which is using the visual and geometric way. It used basic concepts such as areas of squares and rectangles to derive the identity. In the following video, the prerequisite concepts are also included to support the derivation process. The visual proof or geometric representation is shown in detailed and in step-by-step manner. This is for you to easily understand the concept. You may watch the following video:
The same algebraic identity can also be proven using basic algebraic processes. Some of the prerequisite concepts included are multiplication law of indices and distributive property of multiplication. These prerequisites help in the derivation process of the algebraic identity (a+b)^2 = a^2 + 2ab + b^2. You may watch the complete details in this video:
Further, the algebraic identity can also be used as a guide in expanding the square of any binomials. An acronym S-2P-S is introduced in the following video for you to easily remember the process of expanding the square of binomials the fastest way. Here is the complete discussion of the acronym with various examples:
Hope you will learn from these videos about algebraic identities.
Your comments and suggestions are welcome here. Write them in the comment box below. Thank you and God bless!
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PYTHAGOREAN THEOREM EXPLORATION 2 (CUT-OUTS)
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| Pythagorean Theorem Exploration 2 Cutouts |
You may download this template for personal use and for your math class activity. The length of the sides on the second page measures 6.5 inches. This is also the measure of the length of the hypotenuse of the right triangle on the first page.
Your comments and suggestions are welcome here. Write them in the comment box below.
Don't forget to like and share.... :)
Thank you and God bless!
Don't forget to like and share.... :)
Thank you and God bless!
PYTHAGOREAN THEOREM (Exploration 2)
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| The Pythagorean Theorem |
Start with a cutout of a right triangle.
Cut three more cutouts.
Let us name the sides of the right triangle with c as the hypotenuse.
Now, let us form a square using the four (4) triangles. This time, use the hypotenuse as the sides of the square.
Let us take a look at the different parts of the square we formed. If we separate the whole square, we can get its area in terms of c.
The middle part is also a square with sides equal to the difference of sides b and a. The area can be obtained as
On the other hand, the area of the four triangles outlining the sides of the whole square is as follows.
Combining their areas, we obtain
Thus, c^2 = a^2 + b^2.
Your questions, comments and suggestions are welcome here. Kindly write them in the comment box below.
