algebraic expression

Summary - If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If the polynomial can be expressed as the difference of two squares, we u..

Summary - i) An expression of the form a 0 x n + a 1 x n - 1 +....+ a n = 0, where n is a positive integer and a 0 , a 1 ,...,a n belong to some number system F, is called a polynomial in the variable x over F. ii) The degree of polynomial is defined as the highest index of the variable x..

(i) Roster form(i) Roster form (ii) Set builder form (iii) By tables (iv) Arrow diagram (v) By graphs (i) Roster form: The ordered pairs are listed, R = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5)} Where A = {1, 2, 3, 4, 5} and R means 'is twice' in A x A xRy means x = 2y. (i) x = 2y is called the def..

Plot the graph of 2x+3y=9 2x=9-3y (Expressing one variable in terms of the other) Put y = 1, x=3 Put y = -1, x=6 Put y = 7, x=-..

Symmetric Functions - Any expression f( a , b ) involving two numbers a and b is said to be symmetric if it remains unchanged when a and b are interchanged. [i.e. if f( a , b ) = f( b , a )]. Some of the symmetric functions of a and b are All symmetric functions of a and b can be exp..

A formula is formed by using:A formula is formed by using: (a) mathematical symbols and variables (b) given conditions, and (c) simplification. Some well known formulae are listed below: Area of a rectangle A = l x b A = Area l = Length b = Breadth Perimeter of a rectangle P = 2(l + b) P = Perimete..

x 2 - 2x - 48 = x 2 - 8x + 6x - 48 = x(x - 8) + 6(x - 8) = (x - 8) (x + 6) When the coefficient of the highest power is not unity. i.e., type ax 2 bx c, when and b and c are integers. Multiply (3x + 2) (x + 4) and consider the result so obtained. = 3x (x + 4) +2 (x + 4) = 3x 2 + 12x..

The duality principle has many applications. If the dual of an algebraic expression is desired, we simply interchange + and . and replace 1 by 0 and 0 by 1. Let B be a Boolean algebra. Let x, y, z ..

In this chapter, we have learnt the axioms of Boolean algebra. Also, we have learnt about Boolean expressions, their properties and their applications to switching circuits, in particul..

An expression consisting of combinations of binary operations +, . and unary operation and a finite number of elements of a Boolean algebra is called a Boolean functio..