BASIC CONCEPTS OF ALGEBRA
Constant- A
symbol in algebra which has a fixed value, i.e.,
whose value does not change is called a constant.
e.g.- 7, -8, 0,
etc.
Variable- A
symbol which can be assigned different numerical values or whose values vary is
called variable or a literal.
Variables are generally
represented by a letter of the English alphabet as
Note- A combination of a constant and a
variable as :
are also variables as the value of these terms
depend upon the value of
which can change. Hence a combination of a constant
and a variable is always a variable.
Algebraic
expression- A combination of
constants and variables connected by anyone or more of the symbols
is called an algebraic expression.
e.g.-
etc.
Term- A
term is a combination of constants and variables connected together by the
mathematical operators of multiplication and division.
e.g.-
etc., are all terms.
Thus, in an algebraic expression
are terms.
Constant
term-
A term of the expression having no literal factor is called a constant term.
e.g.-
the
constant term is 5.
the
constant term is
.
Like terms-The terms having the
same literal (variable) factors are called like or similar terms.
e.g.-
etc.
Unlike terms-The terms not having
the same literal factors are called unlike or dissimilar terms.
Or, The terms which have
different literal factors.
e.g.-
Various types of algebraic
expressions
1.
Monomials- An expression which
contains only one term is called monomial.
e.g.-
2.
Binomials-An expression containing
two terms is called a binomial.
e.g.-
3.
Trinomials-An expression containing
three terms is called trinomial.
e.g.-
4.
Quadrinomials-An expression containing
four terms is called a quadrinomial.
e.g.-
5.
Polynomials-An expression containing
two or more terms is called a polynomial.
e.g.-
Factor- When two or more numbers
and literals are multiplied then each one of them is called a factor of the
product.
A constant factor is called a numerical
factor, while a literal one is known as a literal factor.
e.g.-
are
factors of term
e.g.-
5
is a numerical factor
Whereas
are
the literal factors.
The numerical
factor is -1 while
and
are literal factors.
Coefficients-In a term of an algebraic
expression, any of the factors with the sign of the term is called the
coefficient of the remaining factors of the product.
e.g.- In the
term
is the coefficient of
is the coefficient of
is the coefficient of
and so on.
Here,
is the numerical coefficient and
is the lateral coefficient.
Substitution-The process of finding
the value of an algebraic expression by replacing the variables (literals) by
their particular values is called substitution.
e.g.- the value
of the expression
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