Archive for September 2020

Visual and Geometric Proof of Algebraic Identities

maths, proofs and derivations, cie math solutions, algebraic identity, algebraic equations, visual proof, geometric proof, algebra, geometric representation

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: