Page 137 - ICSE Math 7

Unlike terms

The terms with different literal factors are known as unlike terms. Example:
2
(a) xy and 2x (b) 3a b and 3ab 2

Coefficient
Any factor in a term is known as the coefficient of the product of the remaining factors. Example:
2
2
2
(a) In the term p q, the coefficient of p = q and the coefficient of q = p .
2
2
2
(b) In the term –3a p, the coefficient of (–3) = a p, coefficient of (–3a ) = p, coefficient of
2
(–3p) = a .
If the factor is a constant, then it is called a numerical coefficient. The factors involving literals are
known as literal coefficients.
Algebraic Expressions

A collection of one or more terms combined together by fundamental operations + or – is known as
an algebraic expression. Example:

(a) In the algebraic expression 3ab + 5 c , there are two terms namely, 3ab and 5 c .

y
y
2
2
2
2
(b) In the algebraic expression 8x + z – , there are three terms namely, 8x , z and – .
z z
There are different types of algebraic expressions based on the number of terms.
An algebraic expression contains variable(s) and constant(s). It cannot be evaluated unless we know
the value of the variable(s). Let’s learn how to form or generate algebraic expressions.
To translate a given statement or situation in algebraic form, replace the words by letters or symbols.
Consider the statement, ‘three times of m increased by 6 equals 40. It can be written in algebraic
expression as 3m + 6 = 40.

Monomial
An algebraic expression which consists of only one term with non-negative integral powers of variables

is known as a monomial. For example, p, 2xy and –3 2
x are monomials.
4
Binomial

An algebraic expression which consists of two terms with non-negative integral powers of variables

4
is known as a binomial. For example, a + b, –3x + y 2 and p 2 – qr are binomials.
2 9 2
Trinomial
An algebraic expression which consists of three terms with non-negative integral powers of variables
r
q
2
2
2
is known as a trinomial. For example, x + z + yz, a + 2ab + b and pq + – are trinomials.
3 5
Polynomial in one variable
An algebraic expression in which the exponents of the variable, say x, are non-negative integers is
called a polynomial in x. A polynomial have finite number of terms. The degree of a polynomial is
the highest power of the literal. For example,

123