Monday, September 28, 2020
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!
------------------------------------------------------------------------------------------------------------- Thank you for your continued support!
Please subscribe and share!
Youtube Channel: CIE Math Solutions
Instagram: @ciemathsolutions
Twitter: @ciemathsolution
Facebook Page: CIE Math Solutions
The algebraic expression "(a+b)^2 = a^2 + 2ab + b^2" is an identity used in mathematics to expand the square of a sum. However, in the field of architecture, this expression itself does not apply directly as a mathematical formula. However, the underlying mathematical principles may be relevant in some contexts.
ReplyDeleteHere is a simplified example of how the principles behind this identity could be applied in an architectural context:
Suppose you are designing a rectangular patio. The total area of the patio can be represented by the square of the sum of its length (a) and its width (b), that is, (a+b)^2. If we expand this, we get:
(a+b)^2 = a^2 + 2ab + b^2
In architectural terms, this could be translated in the sense that the total area of the courtyard is made up of three components: the area of the central rectangular part (a^2), the area of the two rectangles on the sides (2ab), and the area of the corner of the patio (b^2).
Remember that this is just a simplified example to illustrate how mathematical principles can influence architectural concepts. In practice, architecture involves a wide range of calculations and more complex mathematical considerations, such as geometry, proportions, structures, and structural analysis, among others.