We combine variables and constants using the mathematical operations addition and subtraction to construct algebraic expressions.

**Terms
and Co-efficients**

We combine variables and constants using the mathematical
operations addition and subtraction to construct **algebraic
expressions.**

For example, the expression 6*x +* 1 is obtained by adding two parts 6*x* and 1. Here 6*x* and 1 are known as **terms.**
The term 6*x* is a variable and the term 1 is a constant, since
it is not multiplied by a variable. Also we say that 6, *x* are the factors of the term 6*x*.

Similarly, in the expression 3*ab* + 5*c*, the terms are 3*ab* and 5*c*. The factors of the term 3*ab* are 3, *a* and *b*. In the same way, the factors of the term 5*c* are 5 and *c*.

Now let us further try to understand the terms of
an algebraic expression.

Observe the Fig.3.2

What is the perimeter of the given figure?

The perimeter, *'P'* = *x
+* 5 + 6 + *y* + 5 + 4 *+
z + w units,*

= *x
+ y + z + w +* (5 + 6
+ 5
+ 4)

= *x
+ y + z + w +* 20,

where *x,
y, z, w* are variables and 20 is a constant.

Note that, in the above expression, 5 terms are
combined by using addition.

Consider another example as 6*x* − 5*y* + 3. To find the terms of the expression, we write
6*x* + (−5*y*)+3.
Here the terms are 6*x,* (−5*y*) and
3. An expression may have one, two, three or more terms.

Also, a term may be any one of the following:

i) a constant such as 8, −11, 7, −1,…

ii) a variable such as *x,a,p,y,*…

iii) a product of two or more variables such as
*xy, pq, abc, ...*

iv) a product of constant and a variable/variables
such as 5*x,* −7*pq,* 3*abc,*…

** **

**Think**

Can we use the operations multiplication
and division to combine terms?

** **

**Note**

An algebraic expression can have one
term, two terms or more than two terms. An expression with one term is called a
**monomial**, two terms is called a **binomial** and three terms is called a **trinomial**. An expression with one or more terms
is called a **polynomial.
**For example, the expression 2*x*** **is a** ****monomial,**** **2*x*** **+ 3*y*** **is a** ****binomial, **and 2*x* + 3*y* + 4*z* is a **trinomial.** All the expressions given above are polynomials.

** **

**Activity**

To further strengthen the understanding
of variables and constants, let us do the following activity.

Consider, two baskets of cards. One
containing constants and the other containing variables. Pick a constant from the
first basket and a variable from the second basket and form a variable term by expressing
it as a product. Write all the possible terms that can be
constructed using the given constants and variables.

**Answer: **

**Try this**

Complete
the following table by forming expressions using the terms given. One is done for
you.

** **

__Example 3.1__** **

Identify the variables, terms and number
of terms in each of the following expressions:
(i) 12 − *x* (ii) 7 + 2*y* (iii) 29+3*x*+5*y* (iv) 3*x*–5+7*z*

*Solution*

** **

__1.
Co-efficient of a term__

A term of an algebraic expression is a product of
factors. Here each factor or product of factors is called the **co-efficient** of the remaining product of factors.

For example, in the term 5*xy*, 5 is the co-efficient of remaining factor product *xy.* Similarly *x* is the co-efficient
of 5*y*; 5*x* is the co- efficient of *y*. The constant 5 is called the **numerical
co-efficient, **and others are called simply
co-efficients.

A co-efficient can either be a numerical factor
or an algebraic factor or product of both.

Since we often talk about the numerical co -efficients
of a term, if we say “co-efficient”, it will be understood that we are referring
to the numerical co-efficient. If no numerical co-efficient appears in a term, then
the co-efficient is understood to be 1.

Consider the term − 6*ab.* It is the product of three factors −6, *a* and *b* . Also it can be written as a product of two factors
such as −6*a* × *b*, −6*b* × *a* and −6 × *ab*.

The co-efficient of ‘*a*’ is −6*b*

The co-efficient of ‘*b*’ is −6*a*

The co-efficient of ‘*ab*’ is *–* 6

Thus −6 is the **numerical
co-efficient** of the term −6*ab*.

** **

__Example 3.2__

Find the numerical co-efficient of the following terms.
Also, find the co efficient of *x* and *y* in each of the term: 3*x,* −5*xy, −yz, *7*xyz,
y, *16*yx.*

*Solution*

Tags : Algebra | Term 1 Chapter 3 | 7th Maths , 7th Maths : Term 1 Unit 3 : Algebra

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7th Maths : Term 1 Unit 3 : Algebra : Terms and Co-efficients | Algebra | Term 1 Chapter 3 | 7th Maths

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