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**Polynomial identities**are equations that are true for all possible values of the variable. For example, x²+2x+1=(x+1)² is an

**identity**. This introduction video gives more examples of

**identities**and discusses how we prove an equation is an

**identity**.

Moreover, what are valid identities?

If an equation contains one or more variables and is **valid** for all replacement values of the variables for which both sides of the equation are defined, then the equation is known as an **identity**. The equation x ^{2} + 2 x = x( x + 2), for example, is an **identity** because it is **valid** for all replacement values of x.

**Polynomial Equations Formula**Usually, the

**polynomial equation**is expressed in the form of a

_{n}(x

^{n}). Example of a

**polynomial equation**is: 2x

^{2}+ 3x + 1 = 0, where 2x

^{2}+ 3x + 1 is basically a

**polynomial**expression which has been set equal to zero, to form a

**polynomial equation**.

In this way, what are the algebraic identities?

An **algebraic identity** is an equality that holds for any values of its variables. For example, the **identity** ( x + y ) 2 = x 2 + 2 x y + y 2 (x+y)^2 = x^2 + 2xy + y^2 (x+y)2=x2+2xy+y2 holds for all values of x and y.

**Algebraic identity** (a+b)^{2} = a^{2} + 2ab + b^{2} is verified. The **identity** (a+b)^{2} = a^{2} + 2ab + b^{2} is verified by cutting and pasting of paper. This **identity** can be verified geometrically by taking other values of a and b.