Three Variable Identities
The following are algebraic identities involving three variables. These identities can be easily verified by expanding the squares or cubes and performing polynomial multiplication.
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
- a2 + b2 + c2 = (a + b + c)2 – 2(ab + bc + ac)
- a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – ca – bc)
- (a + b)(b + c)(c + a) = (a + b + c)(ab + ac + bc) – 2abc
Algebraic Identities
Algebraic Identities are fundamental equations in algebra where the left-hand side of the equation is always equal to the right-hand side, regardless of the values of the variables involved.
These identities play a crucial role in simplifying algebraic computations and are essential for solving various mathematical problems efficiently. There are many identities in algebra, which we will discuss in this article, including their detailed proof with visuals and algebraically.
Algebraic Identities
Table of Content
- What are Algebraic Identities?
- Algebraic Identities List
- Two Variable Identities
- Three Variable Identities
- Proof of Algebraic Identities
- Solved Examples of Algebraic Identities
- Algebraic Identities Class 8
- Practice Problems on Algebraic Identities