A variable is an alphabet or term that represents an unknown number or unknown value or
unknown quantity. The variables are specially used in the case of algebraic expression
or algebra.
For example, x+9=4 is a linear equation where x is a variable,
where 9 and 4 are constants.
A constant is a value or number that never changes in expression; it's constantly the same.
For example, x = 36 and y = 82 are constant because its face value is 36 and 82 respectively. Its value never changes.
A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables.
For example, in the term 2x, 2 is the coefficient.
Terms which have the same variables are called like terms. Thus, terms having identical variables raised to the same exponent are like terms. So, what is 14x², 11x and 4y called? These are called unlike terms since the variables or exponent raised to these variables are “unlike” or not same.
A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too.
For example, 9x3yz is a single term, where 9 is the coefficient, x, y, z are the variables and 3 is the degree of monomial.
The algebraic expression which contains only two terms is called binomial. It is a two-term polynomial. Also, it is called a sum or difference between two or more monomials. It is the simplest form of a polynomial.
A trinomial is an algebraic expression that has three terms in it.
The examples of trinomials are: x + y + 7. ab + a +b. 3x 2 – 5x + 2.
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).
The degree of an algebraic expression in one variable is the highest exponent of the variable in that expression. The degree of 13 x 6 − 4 x 3 + 3 is 6. The degree of an algebraic expression in more than one variable is the highest sum of the powers of the variables.
Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 34, where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.Exponents and Powers
To factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression are determined and then we group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is its factorization.
The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials. In this way, algebraic identities are used in the computation of algebraic expressions and solving different polynomials.
In mathematics, an algebraic equation or polynomial equation is an equation of the form. P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term algebraic equation refers only to univariate equations, that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables. In the case of several variables (the multivariate case), the term polynomial equation is usually preferred to algebraic equation.
inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly. If we divide an odd number by 2, then it will leave a remainder. The examples of odd numbers are 1, 3, 5, 7, etc. Odd numbers are just the opposite concept of even numbers.
Any number that can be exactly divided by 2 is called as an even number. Even numbers always end up with the last digit as 0, 2, 4, 6 or 8.
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit
A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways: N = {0, 1, 2, 3, ...}
An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.
The whole numbers are the part of the number system which includes all the positive integers from 0 to infinity. These numbers exist in the number line.
A positive number is any number that represents more than zero of anything. Positive numbers include the natural, or counting numbers like 1,2,3,4,5, as well as fractions like 3/5 or 232/345, and decimals like 44.3.
A real quantity having a value less than zero ( < 0 ) is said to be negative. Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e., -2, -100
Negative integers are numbers that have a value less than zero. They do not include fractions or decimals.
For example, -7, -10 are negative integers.
The definition of a positive integer is a whole number greater than zero. The set of positive integers include all counting numbers (that is, the natural numbers)
commutative law is applicable only for addition and multiplication operations. But, it is not applied to other two arithmetic operations, such as subtraction and division. As per commutative law or commutative property, if a and b are any two integers, then the addition and multiplication of a and b result in the same answer even if we change the position of a and b. Symbolically it may be represented as:
Distributive law is a rule of algebra that relates multiplication and addition12. It says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately and then adding the products.