 # Algebraic Expressions Class 7 Notes: Chapter 12

## Introduction to Algebraic Expressions

### Constant

Constant is a quantity which has a fixed value.

### Terms of Expression

Parts of an expression which are formed separately first and then added are known as terms. They are added to form expressions.

Example: Terms 4x and 5 are added to form the expression (4x +5).

### Coefficient of a term

The numerical factor of a term is called coefficient of the term.
Example: 10 is the coefficient of the term 10xy in the expression 10xy+4y.

## Algebra as Patterns

#### For More Information On Algebra as Patterns, Watch The Below Video. To know more about Algebra as Patterns, visit here.

### Writing Number patterns and rules related to them

• If a natural number is denoted by n, its successor is (n + 1).
Example: Successor of n=10 is n+1 =11.
• If a natural number is denoted by n, 2n is an even number and (2n+1) an odd number.
Example: If n=10, then 2n = 20 is an even number and 2n+1 = 21 is an odd number.  To know more about Number patterns, visit here.

### Writing Patterns in Geometry

• Algebraic expressions are used in writing patterns followed by geometrical figures.
Example: Number of diagonals we can draw from one vertex of a polygon of n sides is (n – 3). ## Definition of Variables

• Any algebraic expression can have any number of variables and constants.
• ### Variable

• A variable is a quantity that is prone to change with the context of the situation.
• a,x,p,… are used to denote variables.
• To know more about Variables, visit here.

• ### Constant

• It is a quantity which has a fixed value.
• In the expression 5x+4, the variable here is x and the constant is 4.
• The value 5x and 4 are also called terms of expression.
• In the term 5x, 5 is called the coefficient of x. Coefficients are any numerical factor of a term.

### Factors of a term

Factors of a term are quantities which can not be further factorised. A term is a product of its factors.
Example: The term –3xy is a product of the factors –3, x and y.

## Formation of Algebraic Expressions

• Variables and numbers are used to construct terms.
• These terms along with a combination of operators constitute an algebraic expression.
• The algebraic expression has a value that depends on the values of the variables.
• For example, let 6p2−3p+5 be an algebraic expression with variable p
The value of the expression when p=2 is,
6(2)− 3(2) + 5
⇒ 6(4) − 6 + 5 = 23
The value of the expression when p=1 is,
6(1)− 3(1) + 5
⇒ 6 − 3 + 5 = 8

To know more about Algebraic Expressions, visit here.

## Like and Unlike Terms

### Like terms

• Terms having same algebraic factors are like terms.
Example: 8xy and 3xy are like terms.

### Unlike terms

• Terms having different algebraic factors are unlike terms.
Example: 7xy and −3x are unlike terms.

## Monomial, Binomial, Trinomial and Polynomial Terms

### Types of expressions based on the number of terms

Based on the number of terms present, algebraic expressions are classified as:

• Monomial: An expression with only one term.
Example: 7xy, −5m, etc.
• Binomial: An expression which contains two, unlike terms.
Example: 5mn+4, x+y, etc
• Trinomial: An expression which contains three terms.
Example: x+y+5, a+b+ab, etc.

### Polynomials

• An expression with one or more terms.
Example: x+y, 3xy+6+y, etc.

To know more about Polynomial, visit here.

## Addition and Subtraction of Algebraic Equations

• Mathematical operations like addition and subtraction can be applied to algebraic terms.
• For adding or subtracting two or more algebraic expression, like terms of both the expressions are grouped together and unlike terms are retained as it is.
• Sum of two or more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all like terms.
• Difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms.
• For example, 2y + 3x − 2x + 4y
⇒ x(3−2) + y(2+4)
⇒ x+6y
• Summation of algebraic expressions can be done in two ways:
Consider the summation of the algebraic expressions 5a2+7a+2ab and 7a2+9a+11b
• Horizontal method
5a2+7a+2ab+7a2+9a+11b
= (5+7)a2+(7+9)a+2ab+11b
= 12a2+16a+2ab+11b
• Vertical method
5a2+7a+2ab
7a2+9a+11b
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
12a2+16a+2ab+11b
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

To know more about Addition and Subtraction of Algebraic Equations, visit here.

## Solving an Equation

#### For More Information On Solving an Equation, Watch The Below Video. ### Use of algebraic expressions in the formula of the perimeter of figures

Algebraic expressions can be used in formulating perimeter of figures.
Example: Let l be the length of one side then the perimeter of:
Equilateral triangle = 3l
Square = 4l
Regular pentagon = 5l

### Use of algebraic expressions in formula of area of figures

Algebraic expressions can be used in formulation area of figures.
Example: Let l be the length and b be the breadth then the area of:
Square = l2
Rectangle = l×b = lb
Triangle = $\frac{b\times h}{2}$, where b and h are base and height, respectively.