Page 58 - SM inner class 7.cdr

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A term has several parts like : And the un like terms are 4xy ,– xy since each
(i) Co ef fi cient : The number expressed in of them having the different literal
2
figures or symbol is placed before an coefficients. xy , xy
al ge braic term as a mul ti plier is called its
Types of Algebraic Expressions
co ef fi cient.
Types of algebraic expressions may further be
For ex am ple : In 3abc; 3 is the coefficient of distinguished in the following four categories.
abc, 3a is the coefficient of bc and 3ab is the
co ef fi cient of c. They are: monomial, polynomial, binomial,
trinomial.
(a) Nu mer i cal Co ef fi cient : When one of
the fac tors is an arith me tic num ber, it is 1. Mo no mial: An al ge braic ex pres sion which
always written first and is called a consists of one non-zero term only is called a
mo no mial.
nu mer i cal coefficient.
Ex am ples of mo no mi als :
For Ex am ple : In 3xyz, 3 is the numerical
co ef fi cient of xyz. a is a monomial in one variable a.
2
(b) Lit eral Co ef fi cient : when the co ef fi cient 10 ab is a monomial in two variables a and b.
is ex pressed in let ters, it is called a lateral 5m n is a monomial in two variables m and n.
2
co ef fi cient.
-7 pq is a monomial in two variables p and q.
For ex am ple : In axy is the lit eral co ef fi cient 3
of xy. 5b c is a monomial in two variables b and c.
2b is a monomial in one variable b.
(ii) Con stant Term : A term of the al ge braic
ex pres sion hav ing no lit eral fac tor is 2ax is a monomial in three variables a, x and y.
called a con stant term. 3y
For ex am ple : (i) In 5x + 7, the con stant term is 7. k is a monomial in one variable k.
2
3 -3
2
2
(ii) In a + b - the constant term is 2. Bi no mial : An al ge braic ex pres sion which
4 4 consists of two non-zero terms is called a
The terms which have the same literal bi no mial.
coefficients raised to the same powers but may Ex am ples of bi no mi als :
only differ in numerical coefficient are called m n is a binomial in two variables m and n.
+
like terms.
2
a + 2 b is a binomial in two variables a and b.
For ex am ple :
3
2
5x – 9y is a binomial in two variables x and y.
(i) 3m and –7m are like terms
2
–
3 -11p q is a binomial in two variables p and q.
(ii) z and z are like terms
2 3 c
b + is a binomial in two variables b and c.
The terms which do not have the same literal 2 3
1
coefficients raised to the same powers are 5m n + is a binomial in two variables m and n.
2
2
called unlike terms. 7
For ex am ple : 3. Trinomial : An al ge braic ex pres sion of
q
p
(i) 9 and 9 are unlike terms three non-zero terms only is called a tri nomial.
x y Ex am ples of tri nomial :
(ii) and are unlike terms
3 3 x + y + z is a trinomial in three variables x y,
In algebraic expression and z.
2
2
5x y + 4xy – xy – 9yx 2 2a + 5a + 7 is a trinomial in one variables a.
2
2
2
Here, the like terms are 5x y, – 9yx since xy + x + 2 y 2 is a trinomial in two variables x
each of them having the same literal and y.
2
co ef fi cients x y. -7m 5 + n – 3m n 2 is a trinomial in two
2
3
variables m and n.
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Mathematics In Focus - 7