Basics of Algebra

in algebra we have terms like x² , 5ab, -3a²xy etc. Consider a term (-3a²xy) used in algebra. It has following parts.

Coefficient

The number part of this term i.e. in -3x, (-3) is the coefficient of x.

Variable

The letters or symbols used in an algebraic expression are called variables. ‘a’, ‘x’ and ‘y’ are three distinct variables.

Value of a Variable

A variable may have one or more values in a given situation.

If x2 = 4, then x may have two values (2) and (-2). If a condition that x is a positive number is applied, then the value of x is only one that is (2).

The value of a variable can be changed according to the situation. That’s why they are called variables.

Power or Exponent

In 4x², 2 is power or the exponent of x. in algebra. In general:

Fractions in Power

Same rules of exponents are applied for an algebraic expression if it has power in fraction.

The solution of $\sqrt{\mathrm{-x²}}$ is out of scope of the quantitative section of any general test.

Surds

Expressions such as $\sqrt{2}$, $\sqrt{5}$ , $\sqrt{23}$ cannot be written as numerically exact quantities. Such numbers are called irrational or surds. For example $\sqrt{72}$ in the simplest possible surd can be written as $\sqrt{72}$ = $\sqrt{\mathrm{36\; \times \; 2}}$ = 6$\sqrt{2}$

Constants

All numbers used in an algebraic expression either as exponents, as coefficients or as a term are called constants as they have a fixed value.