Page 134 - ICSE Math 6

Coefficient

Any factor in a term is known as the coefficient of the product of the remaining factors. For example,
2
2
2
(a) In the term x y, the coefficient of x is y and the coefficient of y is x .
2
2
2
2
(b) In the term 15x ab, coefficient of 15 is x ab, coefficient of 15x is ab, coefficient of a is 15x b,
and so on.
Example 5: Separate the following into pairs of like terms.
1 –14
2
2
2xy, –4a, x y, ab, a, 5ab, 6x y, xy
3 15
–14 1
2
2
Solution: The pairs of like terms are 2xy and xy; –4a and a; x y and 6x y; ab and 5ab.
15 3
Example 6: Find the coefficient of xy in each of the following.
2
2
2
2
(a) xy (b) 15a xy (c) 2x y (d) –a bxy
3
2 2
Solution: (a) The factor other than xy is . Therefore, the coefficient of xy is .
3 3
2
2
(b) Factors other than xy are 15 and a . Therefore, 15a is the coefficient of xy.
(c) Factors other than xy are 2 and x. Therefore, 2x is the coefficient of xy.
2
2
(d) Factors other than xy are (–a ) and b. Therefore, –a b is the coefficient of xy.
Algebraic Expressions
A collection of one or more terms combined together by addition or subtraction is known as an
algebraic expression. For example,

Algebraic expression Terms Number of terms Maths Info
ab ab 1
An algebraic expression may
x x
3xy + 3xy, 2 have variables with negative or
a a fractional power.
x 2 –x
2
2
2
2x + y – 2x , y , 3
y y
There are different types of algebraic expressions based on the number of terms. They are:

Monomial
An algebraic expression which consists of only one non-zero term with powers of variables in whole
3
numbers is known as a monomial. For example, a, xy, 5xy, ab, etc., are monomials.
7
Binomial
An algebraic expression which consists of two non-zero terms with powers of variables in whole
numbers is known as a binomial. For example, 3x + a, 5x + 17y, a + b, etc., are binomials.

Trinomial
An algebraic expression which consists of three non-zero terms with powers of variables in whole
2
2
2
2
numbers is known as a trinomial. For example, x + y + 5a, xy + z + 2ab, x – y + z , etc., are trinomials.
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