Identity Dual Operations with 0 and 1 1 X 0 = X (identity) 3 X 1 = 1 (null element) 2 X1 = X 4 X0 = 0 Idempotency theorem 5 X X = XIn the 4 th Chapter of Class 9 RD Sharma Solutions students will study important identities as listed below Algebraic Identities Introduction Identity for the square of a trinomial Sum and difference of cubes Identity These books are widely used by the students who wish to These NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 95 Questions and Answers are prepared by our highly skilled subject experts NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 95 Question 1 Use a suitable identity to get each of the following products
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(x+y)^3 identity class 9
(x+y)^3 identity class 9-18 EXEMPLAR PROBLEMS = 27 9 8 6 33 64 16 × −× − = 0 Since, 3 4 p = 0, so, g(x) is a factor of p(x) Sample Question 2 Find the value of a, if x – a is a factor of x3 – ax2 2x a – 1 Solution 3Let p(x) = x – ax2 2x a – 1 Since x – a is a factor of p(x), so p(a) = 0 ie, a3 – a(a)2 2a a – 1 = 0 a 3 – a 2a a – 1 = 0 3a = 1 = x 2 y 2 z 2 – 6xyz 8 Question 3 Find the following squares by using the identities (i) (b – 7) 2 Solution (b – 7) 2 Using Formula (x – y) 2 = x 2 y 2 – 2xy Putting x = b & y = 7 = b 2 72 – 2(b)(7) = b 2 – 14b 49 (ii) (xy 3z) 2 Solution (xy 3z) 2 Using Formula (a b) 2 = a 2 b 2 2ab Putting a = xy & b
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(x 3) (x – 3) = x 2 – 3 2 = x 2 – 9 Problem Solve (x 5) 3 using algebraic identities Solution We know, (x y) 3 = x 3 y 3 3xy(xy) Therefore, (x 5) 3 = x 3 5 3 3x5(x5) A Computer Science portal for geeks It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions(a)x39 x2 23x15 (b) x36 x2 11x6 Q3 Factorize the following by using a suitable identity (a) 4x2 12xy 9y2 (b) 2a5 – 54 a2 (c) 22x3 3 3 y3 (d) x5 x (e) x6 – y6 (f) (ab)3 (bc)3 (ca)3 (f) x8y8 (g) 27x3135x2 225x 125 Q4 Evaluate the following using a suitable identity
Examples of expressions are x 3, 2y – 5, 3x 2, 4xy 7 etc You can form many more expressions As you know expressions are formed from variables and constants The expression 2y – 5 is formed from the variable y and constants 2 and 5 The expression 4xy 7 is formed from variables x and y and constants 4 and 7 This video shows how to evaluate using the identity '(xy)3=x3y33x2y3xy2'To view more Educational content, please visit https//wwwyoutubecom/appuserie Multiply the following expressions (a) 3xy 2 × (5x 2 y) (b) x 2 yz × xy 2 z × x 2 yz Solution Question 9 Find the area of the rectangle whose length and breadths are 3x 2 y m and 5xy 2 m respectively Solution Length = 3x 2 y m, breadth = 5xy 2 m Area of rectangle = Length × Breadth = (3x 2 y × 5xy 2) sq m = (3 × 5) × x 2 y × xy
Ex 25, 9 Verify (i) x3 y3 = (x y) (x2 – xy y2) LHS x3 y3 We know (x y)3 = x3 y3 3xy (x y) So, x3 y3 = (x y)3 – 3xy (x y) = (x y)3 – 3xy (x y) = (x y) (x y)2 – 3xy) Using (ab)2 = a2 b2 2ab = (x y) (x2 y2 2xy) – 3xy = (x y) (x2 y2 – xy) = (x y) (x2 xy y2) = RHS RHS (x y) (x2 – xy y2) Hence provedFactor x^3y^3 x3 − y3 x 3 y 3 Since both terms are perfect cubes, factor using the difference of cubes formula, a3 −b3 = (a−b)(a2 abb2) a 3 b 3 = ( a b) ( a 2 a b b 2) where a = x a = x and b = y b = y (x−y)(x2 xyy2) ( x y) ( x 2 x y y 2)1 Identify the terms, their coefficients for each of the following expressions In the expression 5xyz 2 – 3zy, the terms are 5xyz 2 and –3zy coefficient of xyz 2 in the term 5xyz 2 is 5 coefficient of zy in the term –3zy is –3 In the expression 1 x x 2, the terms are 1, x and x 2
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CLASSIX MATHEMATICS ASSIGNMENT2 CHAPTER – 2 POLYNOMIALS SECTIONA 1 Write the degree of the given polynomials i) ( 2x 4 )3 ii) ( t3 4 ) ( t3 9 ) 2 Write the coefficient of x4 and x in 4x3 5x4 2x2 3 3 Find the zeroes of f(z)=z2 2z 4 Find the product using suitable identities (4 5x)(45x) 5 WhatProblem Solve (x 3) (x – 3) using algebraic identities Solution By the algebraic identity, x 2 – y 2 = (x y) (x – y), we can write the given expression as;Here, Right hand side = Left hand side which means that (a3) (a3) is an identity Using Activity Method In this method, the algebraic identity is verified geometrically by taking different values of
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The perfect cube forms ( x y) 3 (xy)^3 (xy)3 and ( x − y) 3 ( xy)^3 (x −y)3 come up a lot in algebra We will go over how to expand them in the examples below, but you should also take some time to store these forms in memory, since you'll see them often ( x y) 3 = x 3 3 x 2 y 3 x y 2 y 3 ( x − y) 3 = x 3 − 3 x 2 y 3 Since x − y = 3 xy=3 x − y = 3 implies y = x − 3, y=x3, y = x − 3, substituting this into the given identity gives a x (x − 3) b x c (x − 3) 9 = 0 a x 2 (− 3 a b c) x − 3 (c − 3) = 0 \begin{aligned} ax(x3)bxc(x3)9&=0\\ ax^2(3abc)x3(c3)&=0 \end{aligned} a x (x − 3) b x c (x − 3) 9 a x 2 (− 3 a b c) x − 3 (c − 3) = 0 = 0 If x/2 y3/b2 z3/c2 = (x y z)3/(a b c)2 asked in Class X Maths by priya12 Expert ( 749k points) ratio and proportion
Ex 2 5 12 Verify That X3 Y3 Z3 3xyz 1 2 Ex 2 5
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Rs Aggarwal 19 Solutions for Class 9 Math Chapter 3 Factorisation Of Polynomials are provided here with simple stepbystep explanations These solutions for Factorisation Of Polynomials are extremely popular among Class 9 students for Math Factorisation Of Polynomials Solutions come handy for quickly completing your homework and preparing for exams Chapter 9 NCERT Solutions will be very useful in preparation of the examinations and understanding the concepts properly 1 Identify the terms, their coefficients for each of the following expressions Coefficient in 5xyz 2 is 5 and in 3zy is 3 Coefficient of x and of x 2 is 1 (iii) Terms 4x 2 y 2 , 4x 2 y 2 z 2 and z 2 Question 4 What is the value of a if 2x² x – a is equal to 5 and x = 0 Question 5 Simplify the expression 2 (a² ab) 3 – ab and find its value when a = 5 and b = – 3 Question 6 Using proper identity, find the value of (12)² – (08)² Question 7 Question 8
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Hope the information shed above regarding NCERT MCQ Questions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities with Answers Pdf free download has been useful to an extent If you have any other queries of CBSE Class 8 Maths Algebraic Expressions and Identities MCQs Multiple Choice Questions with Answers, feel free to reach us so Students can also refer to NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities for better exam preparation and score more marks Algebraic Expressions and Identities Class 8 MCQs Questions with Answers Question 1 The expression x 3 is in (a) one variable (b) two variables (c) no variable (d) none of these Answer Identity VII is a 3 b 3 c 3 − 3abc = (a b c) (a 2 b 2 c 2 − ab − bc − ac) Lets take an example a 3 b 3 c 3 − 3abc = (a b c) (a 2 b 2 c 2 − ab − bc − ac) 2 3 3 3 4 3 – 3(2)(3)(4) Chapter 3 Class 9 Coordinate Geometry (Term 1) →
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