In this post we will learn about terms which is the concept commonly used in algebra.
To understand the post, you should have basic knowledge about the concepts of constant and variables.
What is a term in math?
A single mathematical expression is known as terms.
Given are some of the properties of terms:
(a) Term can be constant or variable.
(b) In terms the entity can be single digit or many digits multiplied together.
(c) Entities in the form of addition or subtraction are not single terms.
Examples of Terms
(a) Digit 2
It is a constant term.
(b) Entity y
Here the value of entity y is not fixed, hence it is a variable term.
(c) 10 . x
The entity is a product of constant (10) and variable (x).
It is a single term.
(d) 7. x. y
This entity is also a single term.
It is a product of constant (7) and two variables ( x & y )
(e) 10 x/y
The entity is a single term.
It’s a product of constant 10 and division of two variables ( x and y )
(f) 7x + 3y
The above expression consists of two terms 7x and 3y.
7x ⟹ product of constant 7 and variable x
3y ⟹ product of constant 3 and variable y
(g) \mathtt{10\ x^{2} y^{3}}
The above entity is a single term.
The entity can be written as : 10 . x . x . y . y . y
Hence, it’s a product of constant 10 and variables \mathtt{x^{2} \ .\ y^{3}}
(h) \mathtt{10x\ +\ 3xy}
The above expression consists of two terms; 10x & 3xy.
10x ⟹ made of constant 10 and variable x
3xy ⟹ made of constant 3 and variable x & y
(i) 3x/7 + 2y/5 + 11
The algebraic expression made of 3 terms.
3x/7 ⟹ made of constant 3 & 7 and variable x
2y/5 ⟹ made of constant 2 & 5 and variable y
11 ⟹ made of constant
Terms and Coefficient
The term may consists of multiple constants and variables multiplied together.
For any term the constant number in the front is known as coefficient.
Given below are examples of terms with coefficients:
(a) 5xy
This is a single term with coefficient 5
(b) 10x + 3xy
There are two terms in above expression.
10x ⟹ 10 is the coefficient
3xy ⟹ 3 is the coefficient
(c) \mathtt{9\ .\ x^{2} \ .\ y}
This is a single term with coefficient 9
(d) \mathtt{6xy +\ 10x^{2}}
There are two terms in the expression.
6xy ⟹ 6 is the coefficient
\mathtt{10x^{2}} ⟹ 10 is the coefficient
(e) 15xy – 8yz + 12zx
There are three terms in the expression
15xy ⟹ 15 is the coefficient
-8yz ⟹ -8 is the coefficient
12zx ⟹ 12 is the coefficient
Problems on Terms and Coefficient
(01) Identify the number of terms in below expressions
(a) 7x
(b) 5z – 10x
(c) 3xyz
(d) 2x/3 + 7 + 11y/7
(e) 16x/9 + 5 – 8
(f) \mathtt{3x^{2} y{^{2}} +\ 2y^{3} z^{3}}
(g) \mathtt{\frac{9\mathtt{x^{3} z^{3}}}{11}}
Solution
(a) 7x
Number of terms =1
7x is made of constant 7 and variable x.
(b) 5z – 10x
Number of terms = 2
5z ⟹ is made of constant 5 and variable z
-10x ⟹ is made of constant -10 and variable x
(c) 3xyz
Number of terms = 1
3xyz⟹ is made of constant 3 and variable xyz
(d) 2x/3 + 7 + 11y/7
Number of terms = 3
2x/3 ⟹ is made of constant 2/3 and variable x
7 ⟹ is a constant
11y/7 ⟹ is made of constant 11/7 and variable y
(e) 16x/9 + 5 – 8
Number of terms = 3
16x/9 ⟹ made of constant 16/9 and variable x
5 ⟹ is a constant
-8 ⟹ is a constant
(f) \mathtt{3x^{2} y{^{2}} +\ 2y^{3} z^{3}}
Number of terms = 2
\mathtt{3x^{2} y^{2}} ⟹ made of constant 3 and variable \mathtt{x^{2} and\ y^{2}}
\mathtt{2y^{3} z^{3}} ⟹ made of constant 2 and variable \mathtt{y^{3} and\ z^{3}}
(g) \mathtt{\frac{9\mathtt{x^{3} z^{3}}}{11}}
Number of terms = 1
Its made of constant 9/11 and variable \mathtt{x^{3} and\ z^{3}}
(02) Identify the coefficient of below expressions
(a) 9xy + 22x
(b) 6x
(c) \mathtt{3x^{2} \ +\ 2y^{2}}
(d) \mathtt{\frac{4}{5} x +\ 32y}
(e) 60 + 3y
Solution
(a) 9xy + 22x
Number of terms = 2
9xy ⟹ coefficient is 9
22x ⟹ coefficient is 22
(b) 6x
Number of terms = 1
6x ⟹ coefficient is 6
(c) \mathtt{3x^{2} \ +\ 2y^{2}}
Number of terms = 2
\mathtt{3x^{2}} ⟹ coefficient is 3
\mathtt{2y^{2}} ⟹ coefficient is 2
(d) \mathtt{\frac{4}{5} x +\ 32y}
Number of terms ⟹ 2
\mathtt{\frac{4}{5} x} ⟹ coefficient is 4/5
32 y ⟹ coefficient is 32
(e) 60 + 3y
Number of terms ⟹ 2
3y ⟹ coefficient is 3