Fundamental Concepts & Operations of Algebra
A symbol used to represent an unspecified number is called a LITERAL or a VARIABLE. The small letters a, b, c, x, y, z ………etc of the English alphabet are generally used to indicate a variable.
Numbers like 2, 1/3, -3, and 0 are called CONSTANTS because they have a fixed or constant values.
Operation on Literals –
As literals are also numbers, all the laws of addition, subtraction, multiplication, and division hold for them. Also, these operations can be carried out between literals and numbers. Particular, remember the following -
1) a + b = b + a [ commutative law of addition ]
2) ab = ba [ commutative law of multiplication]
3) a + ( b + c ) = ( a + b ) + c [ Associative law of addition ]
4) a (bc) = (ab) c [ Associated law of multiplication ]
5) a ( b + c ) = ab + ac [ Distributive Law ]
6) a + 0 = a
7) a + (-a) = 0
8) a + a = 2a
9) a + a + a = 3a
10) a . 1 = a
11) a ÷ b = a X --------- = ---------
12) a . --------- = a X --------- = 1
13) a¹ = a
14) a⁰ = 1
A variable multiplied by itself repeatedly is a power of the variable a⁵ is a power of ‘a’, whose base =a and index = 5
The parts of an algebraic expression connected by negative or positive signs are called the terms of the expression. the number of terms in a 1) monomial is 1, 2) binomial is 2, and 3) trinomial is 3.
In a term, the numerical factors is the numerical coefficient and the remaining factor is the literal coefficient.
Two terms are called like terms if their literal factors are the same
An algebraic expression is called a polynomial in ‘a’, if the literal factors of each of its terms is a power of ‘a’, the degree of such a polynomial is the highest index of the power of ‘a’.
The value of an algebraic expression for particular values of the literals is obtained by submitting the appropriate values for the literals.