Algebra Formulas for Class 9 : Algebraic Expressions
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). Algebraic expressions formulas for Class 9 have 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 expressions and identities is introduced. Algebra is one of the most straightforward and high-scoring topics. However, if you don’t recall different Maths formulas for Class 9 Algebra 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 algebraic equations examples with answers on this page. Continue to read on to find out.
List of All 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 all Algebra formulas for Class 9 below:
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]
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.
Class 9 Algebraic Equations: Examples with Answers
Now that we have provided all Algebra formulas for Class 9, let’s see some examples of 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 = (200)2 = 40000 (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 = 90000
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
Here we have provided some of the frequently asked questions related to Maths formulas for Class 9 Algebra:
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: (i) Monomial (ii) Binomial (iii) Trinomial (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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