Algebra Formulas for Class 9: Algebra is a branch of mathematics in which universal symbols and letters are used to represent quantities and numbers in equations and formulas. Algebra is divided into two sections: elementary algebra and modern algebra (Abstract algebra). Algebra formulas for Class 9 comprise formulas relating to algebra identities or expressions. Algebra, along with Geometry and Calculus, is one of the most significant areas of mathematics. All students must have a solid understanding of Algebra in order to comprehend other related subjects. Algebraic Identities for Class 9 has been included in the CBSE curriculum so that students may comprehend the value of Algebra in their daily lives.
In CBSE Class 9, the chapter on algebraic identities is introduced. Algebra is one of the most straightforward and high-scoring topics. However, if you don’t recall the different Algebra Formulas for Class 9 and how to use them in Algebraic Expressions and identities, it can get a bit tough. To make it easier for students, we have included the entire collection of formulas on a single page. Continue reading to find out. This is a difficult chapter in which one must memorise all of the formulas and apply them correctly. Embibe provides all of the formulas on a single page to make it easier for them. We feel that algebra formulas for class 9 will help students score higher in maths. Scroll down to find more.
List of Algebra Formulas for Class 9
Students who are looking for the complete list of Maths formulas for Class 9 Algebra can refer to this article. We have also provided a one-click downloadable PDF below these formulas.
|1. (a + b)2 = a2 + 2ab + b2|
2. (a − b)2 = a2 − 2ab + b2
3. (a + b)(a – b) = a2 – b2
4. (x + a)(x + b) = x2 + (a + b)x + ab
5. (x + a)(x – b) = x2 + (a – b)x – ab
6. (x – a)(x + b) = x2 + (b – a)x – ab
7. (x–a)(x–b) = x2 – (a+b)x + ab
8. (a + b)3 = a3 + b3 + 3ab(a + b)
9. (a – b)3 = a3 – b3 – 3ab(a – b)
10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz − xz)
15. x2 + y2 = 12[(x + y)2 + (x – y)2]
16. (x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc
17. x3 + y3 = (x + y)(x2 – xy + y2)
18. x3 – y3 = (x – y)(x2 + xy + y2)
19. x2 + y2 + z2 − xy – yz –zx = 1/2[(x − y)2 + (y − z)2 + (z − x)2]
Maths Algebraic Identities for Class 9
Do you know the difference between an algebraic formula (identity) and an algebraic expression? An algebraic formula is an equation that is a rule written using mathematical and algebraic symbols. It always involves algebraic expressions on both sides. Moreover, equality will hold true for any values of variables.
On the other hand, an algebraic expression is not separated by an equal sign. An algebraic expression contains two things – Variables and Constants. The value of the variable changes in different expressions while the constant remains the same. We can understand the difference between the two from the following example:
(a + b)2 =a2 + 2ab + b2 is an algebraic formula and here,
(a + b)2 is an algebraic expression.
a2+ 2ab + b2 is an algebraic expression.
The LHS and RHS of an algebraic formula are always equal for any value of the variables in it. This property allows us to deduce the result on RHS if we know the values to the left of an expression.
Check out other important Maths articles for Class 9:
|NCERT Solutions for Class 9 Maths||Class 9 Maths Syllabus|
|NCERT Books for Class 9 Maths||Maths Formulas for Class 9|
Algebraic Identities For Class 9 With Examples
Now that we have provided all the formulas of Algebra Class 9, let’s see some examples on the same:
|Question 1: Evaluate each of the following using identities:|
(i) (2x – 1/x)2
(ii) (2x + y) (2x – y)
Answer: (i) (2x – 1/x)2
Using identity: (a – b)2 = a2 + b2 – 2ab, we get:
(2x – 1/x)2
= (2x)2 + (1/x)2 – 2 (2x)(1/x)
= 4x2 + 1/x2 – 4
(ii) (2x + y) (2x – y)
Using identity: (a – b)(a + b) = a2 – b2, we get:
(2x + y) (2x – y)
= (2x )2 – (y)2
= 4x2 – y2
|Question 2: Simplify the following:|
(i) 175 x 175 +2 x 175 x 25 + 25 x 25
(ii) 322 x 322 – 2 x 322 x 22 + 22 x 22
Answer: (i) Using identity: a2+ b2+2ab = (a+b)2, we get:
175 x 175 +2 x 175 x 25 + 25 x 25
= (175)2 + 2 (175) (25) + (25)2
= (175 + 25)2
(ii) Using identity: a2+ b2-2ab = (a-b)2, we get:
322 x 322 – 2 x 322 x 22 + 22 x 22
= (322)2 – 2 x 322 x 22 + (22)2
= (322 – 22)2
|Question 3: If m + 1/m = 11, find the value of m2 +1/m2. |
Answer: m + 1/m = 11 (Given)
So, (m+1/m)2 = m2 + 1/m2 + 2 x m x 1/m
⟹ (m+1/m)2 = m2 + 1/m2 + 2
⟹ (11)2 = m2 + 1/m2 + 2
⟹ 121 = m2 +1/m2 + 2
⟹ m2 +1/m2 = 119
|Question 4: Write the following in the expanded form: |
(i) (a + 2b + c)2
(ii) (a2 +b2 +c2) 2
(iii) (a/bc + b/ac + c/ab) 2
Answer: Using identity: (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz, we can expand the algebraic expressions.
(i) (a + 2b + c)2
= a2 + (2b) 2 + c2 + 2a(2b) + 2ac + 2(2b)c
= a2 + 4b2 + c2 + 4ab + 2ac + 4bc
(ii) (a2 +b2 +c2) 2
= (a2) 2 + (b2) 2 + (c2 ) 2 + 2a2 b2 + 2b2c2 + 2a2c2
= a4 + b4 + c4 + 2a2 b2 + 2b2 c2 + 2c2 a2
(iii) (a/bc + b/ac + c/ab)2
= (a/bc)2 + (b/ac)2 + (c/ab)2 + 2(a/bc)(b/ac) + 2(b/ac)(c/ab) + 2(c/ab)(a/bc)
= a2/b2c2 + b2/c2a2 + c2/a2b2 + 2/a2 + 2/b2 + 2/c2
Check Algebra Formulas for other classes as well:
|Algebra Formulas for Class 8||Algebra Formulas for Class 10 (Soon)|
Practice Questions on Algebraic Expressions Formulas for Class 9
Here we have provided some of the practice questions on formula of Algebraic Expression for Class 9:
Question 1: Factorize the following algebraic expressions:
(i) x3 + x – 3x2 – 3
(ii) a(a + b)3 – 3a2b(a + b)
(iii) x(x3 – y3) + 3xy(x – y)
(iv) a2x2 + (ax2 +1)x + a
Question 2: What are the possible expressions for the dimensions of the cuboid whose volume is 3x2 – 12x.
Question 3: Resolve into factors for the following algebraic expressions:
(i) (x + 2)(x2 + 25) – 10x2 – 20x
(ii) 2a2 + 26–√ ab +3b2
(iii) a2 + b2 + 2(ab + bc + ca)
(iv) 4(x – y)2 – 12(x -y)(x + y) + 9(x + y)2
Question 4: Find the H.C.F and L.C.M of the following expressions:
(i) a2 + 2ab + b2
(ii) b2 – a2 + 2bc + c2
(iii) – b2+ a2 + 2ca + c2
FAQs on Class 9 Algebra Formulas
Here we have provided some of the frequently asked questions related to the Class 9 Algebra formula:
|Q1: How to derive algebraic expressions?|
Ans: An algebraic expression is a combination of constants, variables, and algebraic operations (+, -, ×, ÷). We can derive the algebraic expression for a given situation or condition by using these combinations.
|Q2: What is the difference between an algebraic expression and a polynomial?|
Ans: The difference between polynomial and algebraic expressions is that polynomials include only variables and coefficients with mathematical operations (+, -, ×) but algebraic expressions include irrational numbers in the powers as well.
Moreover, polynomials are continuous function (e.g: x2 + 2x + 1) but algebraic expression may not be continuous sometimes (e.g: 1/(x2 – 1) is not continuous at 1).
|Q3: What are the types of algebraic expressions?|
Ans: Algebraic expression can be one of the following types:
(iv) Linear polynomial
(v) Quadratic polynomial
(vi) Cubic polynomial
|Q4: Is 5x an algebraic expression?|
Ans: Yes, any expression containing variables, numbers, and operation symbols is called an algebraic expression. So, 5x is an algebraic expression. It is also a monomial because it contains only one term.
|Q5: What are the basic laws of algebra?|
Ans: The basic laws of algebra are the associative, commutative, and distributive laws. Check the following table to understand the laws.
Now you are provided with all the necessary information regarding Maths formulas for Class 9 Algebra. Students can make use of NCERT Solutions for Maths provided by Embibe for their exam preparation.
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