Algebraic Expressions Class 7 Notes CBSE Maths Chapter 12 (Free PDF Download)

Terminologies:

• A constant is a defined as a term having fixed numeral value. e.g., $8,23,\sqrt{21},4\dfrac{3}{2}$ etc.

• A variable or literal is the term that does not have any fixed value and can be replaced or assigned with a constant as per requirement. e.g., $x,a,y,b,z$ etc.

• A term can be a numeral or a variable or combination (product or quotient) of both numerals and variables. e.g., $7,x,5y,6ax,\dfrac{18}{zx},\dfrac{ab}{c}$ etc.

• A term is a product of factors. The term $4xy$ in the expression $4xy+7$ is a product of factors $x,y$ and $4$. Factors that containing variable are said to be algebraic factors.

• Terms which have the same algebraic factors are known as like terms whereas the terms which have different algebraic factors are unlike terms. Thus, terms $4xz$ and $-3xz$ are like terms; but terms $7xy$ and $-8x$ are not like terms. Although multiplication and division operations can be performed for both like and unlike terms.

• The coefficient of any term in an expression is the numerical factor in that term. Sometimes any one factor in a term is called the coefficient of the remaining part of the term.

• Expressions are made up of terms. Terms are added to make an expression. For example, the addition of the terms $4xy$ and $7$ gives the expression $4xy+7$. An expression that has one or more terms is called a polynomial.

• Monomials are one-term expressions, binomials are two-term expressions and trinomials are three-term expressions.

Algebraic Expressions:

Algebraic expressions are formed from variables and constants. To form algebraic expressions we use the basic algebraic operations of addition, subtraction, multiplication and division on the variables and constants. For example, the expression $4xy+7$ is formed from the variables $x$ and $y$ and constants $4$ and $7$. The constant $4$ and the variables $x$ and $y$ are multiplied to give the product $4xy$ and the constant $7$ is added to this product to give the expression.

Addition And Subtraction Of Algebraic Expressions:

• When we add like terms then final result gives another like term with the numerical coefficient equal to the sum of coefficients of all like terms. e.g., $4xy+5xy=(4+5)xy=9xy$.

• Like terms when subtracted gives another like term with the numerical coefficient equal to the difference of coefficients of all like terms. e.g., $4xy-5xy=(4-5)xy=-xy$.

• Unlike terms can neither be added nor subtracted like the like terms.

• When two algebraic expressions are added or subtracted, we put the like terms together and keep the unlike terms as it is. And then perform the required operations. e.g., the sum of $(3x+13+9xy)$ and $(5xy-8z-2x)$ will be

$(3x+13+9xy)+(5xy-8z-2x)$

$=(9+5)xy+(3-2)x+13-8z$

$=14xy+x-8z+13$

Finding Value Of An Expression:

The exact or numeral value of an algebraic expression always depends on the values of variables in that expression. Generally, the value of an expression is determined when we need to check if a particular value satisfies a given equation. Values of expressions are also determined when we use formulas from everyday mathematics and geometry. For example, the area of a square is given by the formula ${{a}^{2}}$, where $a$ is the length of its side. So, if the length of side is given as $2cm$, then the area will be ${{(2cm)}^{2}}=4c{{m}^{2}}$.

Using Algebraic Expressions:

• Perimeter formulas: Perimeter of any polygon is its circumferential length and can be determined by adding the lengths of each of its sides. For regular polygons where the length of each side is the same, the perimeter can simply be determined by multiplying the length of one side with the number of sides of the polygon. For example, consider $l$ as the length of a side of a regular polygon, then for an equilateral triangle, the perimeter will be $3l$, for a square or rhombus will be $4l$, for a regular pentagon will be $5l$ and so on.

• Area formula: Area of a square with one of its sides having length $l$ is given by ${{l}^{2}}$. Similarly, for a triangle with base length $b$ and height $h$, area is given by $\dfrac{b\times h}{2}$. And the area of a rectangle with length $l$ and breadth $b$ is given by $lb$.

• Rules for number patterns: General terms of different progressions or series of numbers are denoted using algebraic expressions. For example, suppose $n$ is any natural number, then $2n$ will be an even number and $2n+1$ will be an odd number. Similarly, to find out the terms in multiples of 5 we can denote the sequence as $5,10,15,......,5n,....$.

• Geometrical patterns – The number of diagonals in a polygon can be determined by the expression $(n-3)$, where $n$ is the number of sides of that polygon. The Sum of interior angles of a regular polygon can be determined by the expression $(n-2)\times {{180}^{\circ }}$.

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About Class 7 Chapter 12 Algebraic Expression

Chapter 12 Algebraic expression focuses on the formation of expression. In your previous class V1, you must have studied how algebraic expressions are used to formulate puzzles and problems. You must have also seen examples of several expressions in the chapter simple equation.

Expressions are important concepts of Algebra. In Class 7 Chapter 12 Algebraic Expression, you will study how expressions are formed, how expressions can be combined, how we can find the algebraic expression values, and how they can be used.

Chapter 12 Algebraic Expression includes a total of 4 exercises and 8 sections. Let us discuss the important topics covered in different sections.

• 12.1 - Introduction of the Chapter

• 12.2 - How Expressions are Formed 

• 12.3 - Terms of an Expressions

• 12.4  - Like and Unlike terms

• 12.5 - Monomials, Binomials, Trinomials, and Polynomials

• 12.6 -  Addition and Subtraction of Algebraic Expressions

• 12.7 - Finding the Value of an Expression

• 12.8 -  Using Algebraic Expressions - Rules and Formulas 

The formulas and rules covered in sections 12.8 are:

• Perimeter Formulas

• Area Formulas

• Rules for Number Pattern

• Pattern in Geometry

Class 7 Chapter 12 Algebraic Expression is important as it helps students to learn how algebraic expressions are formed and the way variables, constant, and arithmetic operations are used to form algebraic expressions. It also helps students to learn how to draw tree diagrams with the help of factors and terms of different algebraic expressions. To have a better understanding of the chapter, it is recommended to download Ch 12 Class 7 Maths Revision Notes free PDFs now.

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