What Are Algebraic Identities?
An algebraic identity is basically an equation in which L.H.S. equals R.H.S. for all values of the variables. An identity in math is an equation that holds true for all the values, even if you change the variables involved. For every value of the variables, an algebraic identity indicates that the left and right sides of the equation are identical.
Algebraic identities are equations that hold true for all values of variables.
In mathematical identities, the values on the left and right sides of the equation are exactly the same. We use algebraic identities as a set of formulas that help us in simplifying and solving algebraic equations.
Consider an example.
To expand the algebraic expression (x+1)^2, you will have to multiply (x+1) with itself. It will surely be lengthy and time consuming. However, if you use the algebraic identity (a+b)^2=a^2+2ab+b^2, you will simply have to substitute the values and your job is done!
Most Important Algebraic Identity
Algebraic Identity 1: ( a + b )^2 = a^2 + 2ab + b^2.
Algebraic Identity 2: ( a − b )^2 = a^2 − 2ab + b^2.
Algebraic Identity 3: ( x + a ) ( x + b ) = x^2 + (a + b) x + ab.
Algebraic Identity 4: ( a + b ) ( a − b ) = a^2 − b^2.
Proof
Algebraic Identity 1: ( a + b )^2 = a^2 + 2ab + b^2.
Algebraic Identity 2: ( a − b )^2 = a^2 − 2ab + b^2.
Algebraic Identity 3: ( x + a ) ( x + b ) = x^2 + (a + b) x + ab.
Algebraic Identity 4: ( a + b ) ( a − b ) = a^2 − b^2.