Algebraic identities can be defined as algebraic equations that are always valid for whatever amount of their variables. Algebraic identities are used in the solution of polynomials. On both sides of the equation, variables and constants are present. The left side of an algebraic identity is equal to the right side of the equation. Algebraic identities are therefore utilized in the calculation of algebraic expressions and the solution of various polynomials. You might already have studied a handful of them in rudimentary classes. In this post, we will review them and present you with some more common algebraic identities and provide illustrations.
Difference between an algebraic expression and algebraic identities
An algebraic expression has variables and constants. Variables in expressions can have any value. As a result, if the variable values change, the expression value may change. However, the algebraic identity is symmetric, which makes sense for all continuous variables. There is an equal sign between the terms of an algebraic identity. For an equation to be an algebraic identity, both sides of the equality sign must pertain to a similar value. If the value of the expression is, let’s say, 5 on the left side, then the value of the algebraic identity on the right ought to be 5. The algebraic identity can also be solved using various methods to identify the values of the unknown variables.
The Substitution Method
The Activity Method
All the algebraic identities are derived from a single theorem known as the binomial theorem. Some of the important identities that must be remembered all the time are listed below:
|Identity I:||(k + l)2 = k2 + 2kl + l2|
|Identity II:||(k - l)2 = k2 - 2kl + l2|
|Identity III:||k2 – l2= (k + l) (k – l)|
|Identity IV:||(x + k) (x + l) = x2 + (k + l) x + kl|
|Identity V:||(k + l + m)2 = k2 + l2 + m2 + 2kl + 2lm + 2mk|
|Identity VI:||(k + l)3 = k3 + l3 + 3kl (k + l)|
|Identity VII:||(k – l)3 = k3 – l3 – 3kl (k – l)|
|Identity VIII:||k3 + l3 + m3 – 3klm = (k + l + m) (k2 + l2 + m2 – kl – lm – mk|