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Algebra is a part of Mathematics in which general symbols and letters are used to represent quantities and numbers in equations and formulae. There are two parts in algebra – Elementary algebra and Modern algebra (Abstract algebra). Algebra formulas for class 9 include formulas related to algebra identities or expressions.
Algebraic identities chapter is introduced in CBSE class 9. This is a tricky chapter where one needs to learn all the formula and apply them accordingly. To make it easy for them, Tam Tai Duc provide all the formulas on a single page. We believe, algebra formulas for class 9 will help students to score better marks in mathematics.
List of Algebra Formulas for Class 9
Algebra Formulas List is given below. Have a look at it.
Algebraic Identities For Class 9
- a2 – b2 = (a – b)(a + b)
- (a + b)2 = a2 + 2ab + b2
- a2 + b2 = (a + b)2 – 2ab.
- (a – b)2 = a2 – 2ab + b2
- (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – b3 – 3ab(a – b)
- a3 – b3 = (a – b)(a2 + ab + b2)
- a3 + b3 = (a + b)(a2 – ab + b2)
- x(a + b) = xa + xb
- x(a – b) = xa – xb
- (x – a)(x – b) = x2 – (a + b)x + ab
- (x – a)(x + b) = x2 + (b – a)x – ab
- (x + a)(x – b)= x2 + (a – b)x – ab
- (x + a)(x + b)= x2 + (a + b)x + ab
- (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
- (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2zx
Applications of Algebra Formulas Class 9
Understanding the basics of algebra formulas class 9 forms the foundational knowledge for higher grades. It helps students to learn various topics like trigonometry, calculus, geometry, etc. Algebra formulas also form the core of various real life calculations and analyses. Let us have a brief idea about the applications of class 9 algebra formulas in the real world.
- Algebra formulas class 9 are applied in real life to budget our expenses for savings. These formulas help us in making wiser decisions while spending our money.
- By evaluating the options through algebraic formulas, we can easily find out the best deals on everything from insurance to buying things to save money.
- Algebraic formulas are applied for recipes and cooking meals. Analyzing the right quantity of ingredients requires algebraic calculations.
- Algebra formulas are applied in planning and estimation. For instance, for guessing the amount of paint required to color the roof, we can simply calculate the area of the rectangular roof to know the exact quantity.
Tips to Memorize Algebra Formulas Class 9
The shift from basic arithmetic to algebra formulas in class 9 and symbolic representation might initially seem intimidating for students. However, gradually they can grasp these formulas with practice and some math tricks. Here are some tips for students to memorize these formulas in much easier ways:
- Algebra class 9 formulas deal with terms like real roots, equal roots, imaginary roots, determinants, etc. The students must make sure that they understand the meaning of the necessary terms before memorizing these formulas. They can get help from teachers or their friends to get clarity on the same.
- After having a crystal clear knowledge of the terms used in the formulas, the students can try to use some fun tricks like phrases to remember them better. Also, the students can put the formula images as wallpaper on their gadgets which will ensure a quick revision whenever they use their mobile or laptop.
- Students should practice lots and lots of problems and examples provided in the textbook to use these class 9 algebra formulas.
Algebra FormulasClass 9 Examples
Example 1: Factorise: 216x3 – 27y3
Solution: 216x3 – 27y3 = (6x)3 – (3y)3
By applying the formula of a3 – b3 = (a – b) (a2 + ab + b2 ), we obtain
216x3 – 27y3 = (6x – 3y) (36x2 + 18xy + 9y2 )
Students can download the printable Maths Formulas Class 9 sheet from below.
FAQs On Algebra Formulas Class 9
What are the Important Algebra Formulas Class 9?
Some of the most important algebra formulas class 9 are as follows:
- (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – b3 – 3ab(a – b)
- a3 – b3 = (a – b)(a2 + ab + b2)
- a3 + b3 = (a + b)(a2 – ab + b2)
- x(a + b) = xa + xb
- x(a – b) = xa – xb
What are the Basic Topics covered under Class 9 Algebra?
The basic topics covered under class 9 algebra helps students identify the type of polynomial, solution of a polynomial equation, roots and factors of the polynomial equations. Also, these basic formulas help to implement a clear knowledge of all the types of polynomial equations. The list of all basic algebra class 9 formulas is provided in this article.
Why is it Important to Solve all Questions Based on Algebra Class 9 Formulas?
It is important to solve all questions based on algebra class 9 formulas to understand how to evaluate different types of polynomial equations and expressions. It helps students to prepare well for exams and implement a clear understanding of all core topics.
How Many Formulas are there in Algebra Class 9?
There are around 8 formulas in algebra class 9 that can be remembered easily if the students follow the tips mentioned in this article on a consistent basis. The key algebra formulas included in the class 9 maths are based on calculating the roots of various algebraic expressions and equations.
How can I Memorize Algebra Class 9 Formulas?
One of the best ways to memorize class 9 algebra formulas is to have a clear understanding of all the terms involved in the formulas. Once the students form a deep conceptual understanding of the topic they can easily memorize them. One must also ensure to prepare all the solved examples of the textbook by applying these formulas. This will provide the most comprehensive coverage on formula usage in various contexts.
What are the algebraic identities of Class 9? Why are they used?
Algebraic identities are the equalities that are eternally true irrespective of the true values chosen by the user. These identities use variables that can take any values. They are the generalised equality statements. Algebraic identities are used in the factorisation of polynomial equations. They are also used in finding the squares and cubes of larger numbers such as numbers in several hundreds and thousands and also smaller numbers of few decimal points. Algebraic identities can be proved by theoretical calculations and also by activity methods.
Distinguish between algebraic expressions and algebraic identities?
An algebraic expression is a mathematical representation of statements in the form of variables and constants. An expression may not take the same values in all instances. The value of an expression changes with the value of the variable. An algebraic identity is a mathematical representation of statements that can be equated to the other statements. They are general equality statements used to solve various types of algebraic expressions. The value of a particular algebraic identity gives the same equality relationship irrespective of the values assigned for the variable.
Identities of Maths Class 9 Problems
1. Evaluate the square of 99 and 101 using appropriate algebraic identity.
Solution:
992 = (100 – 1)2 and 1012 = (100 + 1)2
992 can be solved using the algebraic identity (a – b)2 = a2 + b2 – 2ab.
a = 100 and b = 1
(a – b)2 = a2 + b2 – 2ab
(100 – 1)2 = 1002 – 2 x 100 x 1 + 12
= 10000 + 1 – 200
= 9801
1012 can be solved using the algebraic identity (a + b)2 = a2 + b2 + 2ab.
a = 100 and b = 1
(a + b)2 = a2 + 2ab + b2
(100 + 1)2 = 1002 + 2 x 100 x 1 + 12
= 10000 + 200 + 1
= 10201
2. If the sum of two numbers is 12 and the sum of their cubes is 468, find the product of these numbers using algebraic identities.
Solution:
Let us consider the two numbers as ‘a’ and ‘b’.
Sum of the numbers = a + b = 12
Sum of their cubes = a3 + b3 = 468
Product of these two numbers = ab =?
The product of two numbers can be found using the algebraic identity:
(a + b)3 = a3 + b3 + 3ab (a + b)
(12)3 = 468 + 3ab (12)
1728 = 468 + 3ab (12)
36 ab = 1728 – 468
36 ab = 1260
ab = 1260 / 36
ab = 35
The product of two numbers is 35.
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