Algebraic Identities

What is meant by an Algebraic Identity?

Consider 2x + 3 = 9.

Let us find x.                           

2x = 9 – 3 = 6      {remember transposition rule?}

x = 6/2 = 3.

So, the value of x for which 2x + 3 is equal to 9 is 3.

Now, 3 is called solution or root of the linear equation 2x + 3 = 9

We say 3 satisfies the given linear equation 2x + 3 = 9

Also, no other value of x satisfies the given linear equation.  

Now, consider the following:

(x + 1)2 = x2 + 2x + 1

The two sides, L.H.S. and R.H.S. are equal for any value of x.

Substitute x with any number, the two sides will be always equal.  

Hence, (x + 1)2 = x2 + 2x + 1is called an identity

Definition of an Algebraic Identity

An algebraic expression which holds for any value of the variable, typically x, is called an Algebraic Identity.

An algebraic expression, in which the two sides, i.e., L.H.S. and R.H.S. are equal on substituting any value for the variable, is called an Algebraic Identity. 

Algebraic Identities are simple Operations on Polynomials.

Though, operations on polynomials were already dealt earlier, still they will be considered here once again as special products in light of Algebraic Identities.

Algebraic Identity (Identities)

Algebraic identities are special products of polynomials. Therefore, let us consider the product of various types of polynomials.