Algebraic identities are one of the various concepts that are used to make the complex equation simpler. As we are not allowed to use calculators in the exam, we have found an easy way to reduce the efforts to solve complex mathematical expressions. Most of the algebraic identities are used for the multiplication of polynomials or finding out their squares etc. There are heaps of algebraic identity formulas.
Mainly the formulas we will be using consist of variables that can take any desired value, be it a large number or a small number. Algebraic equations are very useful for mathematical calculations or scientific expressions. For example, they are used to find out the squares, cubes, solutions to various equations, easy solutions to binomial expansion raised to the power of two or three etc. Algebraic identities are used for the factorisation of polynomial equations as well.
There is a difference between algebraic identities and algebraic expressions. An algebraic expression is nothing but a representation of statements in the form of either constants or variables. The value of the expression may change with the values of variables but whereas algebraic identities are the mathematical representation of the statements that helps to equate other statements. They are generally used to solve several types of algebraic expressions. But one thing to remember, the value of a particular algebraic identity gives us the same equality relationship, which does not depend on the values assigned to the variables.
Some theoretical calculations can prove algebraic identities. For example, like terms are formed from the same variables, and the powers of these variables also remain the same. However, coefficients of like terms need not remain the same. For example, in adding or subtracting polynomials, we've to look for the like terms and add or subtract them. Then, we have to handle the, unlike terms. Moreover, sometimes we need to multiply algebraic expressions: for example, finding a rectangle area, which is further discussed in the chapter.