Tuesday, May 4, 2021

Polynomial Division | Division of Polynomial | Division Algorithm for Polynomials in hindi

Polynomial Division | Division of Polynomial | Division Algorithm for Polynomials in hindi

Polynomial Division | Division of Polynomial | Division Algorithm for Polynomials in hindi

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Polynomial Division | Division of Polynomial | Division Algorithm for Polynomials in hindi


Polynomial Division | Division of Polynomial | Division Algorithm for Polynomials in hindi Class: 10th Subject: Maths Chapter: Polynomials Topic Name: Division Algorithm for Polynomials Points covered in this video:- From Euclid’s division lemma, we know that Dividend = (Divisor x Quotient) + Remainder Applying the same to polynomials, If f(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that f(x) = q(x) x g(x) + r(x), Degree of r(x) less than Degree of g(x) If r(x) = 0, then polynomial g(x) is a factor of polynomial f(x). Class 10 Maths Chapter 2 Polynomials | Division Algorithm for Polynomials class 10 maths chapter 2 polynomials,division algorithm for polynomials, maths polynomials,polynomials class 10,polynomial division in hindi,division algorithm for polynomials class 10 maths,division algorithm for polynomials class 9,class 10 maths chapter 2,polynomials in maths,polynomials in 9 maths,polynomials,polynomials in class 10,polynomials division algorithm class 10 maths,polynomials division algorithm class 10,division algorithm class 10,Style stardum MS, algebric expressions class 8,division of polynomials,division of polynomials class 8,division of algebraic expressions,algebra division,algebra divide,division of algebraic expressions class 8,algebraic expressions class 7,how to divide polynomials,division of polynomial by another polynomial,बहुपद का भाग,long division of polynomials,introduction algebraic expressions,polynomial long division, division of polynomials class 8 Algebraic expressions class 8 division of algebraic expressions class 8 algebra divide class 8 division of polynomials how to divide algebraic expressions algebra division Polynomial division algebra ka bhag division of polynomial division method how to divide polynomials algebraic expressions algebraic expressions class 7 algebra class 8 polynomial divide polynomial division class 9 polynomial class 9 #polynomial #maths #division #mathematics #Class10

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Monday, May 3, 2021

Algebraic Identities ll algebraic Expressions ll CBSE ICSE maths class 8 class 9 class 10 in hindi

Algebraic Identities ll algebraic Expressions ll CBSE ICSE maths class 8 class 9 class 10 in hindi

Algebraic Identities ll algebraic Expressions ll CBSE ICSE maths class 8 class 9 class 10 in hindiा

 

Algebraic Identities ll algebraic Expressions ll CBSE ICSE maths class 8 class 9 class 10 in hindi


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Algebraic Identities

The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials. In this way, algebraic identities are used in the computation of algebraic expressions and solving different polynomials. You have already learned about a few of them in the junior grades. In this article, we will recall them and introduce you to some more standard algebraic identities, along with examples.

Standard Algebraic Identities List

All the standard Algebraic Identities are derived from the Binomial Theorem, which is given as:

(a+b)n=nC0.an.b0+nC1.an1.b1+..+nCn1.a1.bn1+nCn.a0.bn

Some Standard Algebraic Identities list are given below:

Identity I: (a + b)2 = a2 + 2ab + b2

Identity II: (a – b)2 = a2 – 2ab + b2

Identity III: a2 – b2= (a + b)(a – b)

Identity IV: (x + a)(x + b) = x2 + (a + b) x + ab

Identity V: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

Identity VI: (a + b)3 = a3 + b3 + 3ab (a + b)

Identity VII: (a – b)3 = a3 – b3 – 3ab (a – b)

Identity VIII: a3 + b3 + c– 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)

 

Example 1: Find the product of (x + 1)(x + 1) using standard algebraic identities.

Solution: (x + 1)(x + 1) can be written as (x + 1)2. Thus, it is of the form Identity I where a = x and b = 1. So we have,

(x + 1)2 = (x)2 + 2(x)(1) + (1)= x+ 2x + 1

 

Example 2: Factorise (x4 – 1) using standard algebraic identities.

Solution: (x4 – 1) is of the form Identity III where a = x2 and b = 1. So we have,

(x4 – 1) = ((x2)2– 12) = (x+ 1)(x– 1)

The factor (x– 1) can be further factorised using the same Identity III where a = x and b = 1. So,

(x4 – 1) = (x+ 1)((x)–(1)2) = (x+ 1)(x + 1)(x – 1)

 

Eample 3: Factorise 16x2 + 4y+ 9z2 – 16xy + 12yz – 24zx using standard algebraic identities.

Solution: 16x2 + 4y+ 9z2– 16xy + 12yz – 24zx is of the form Identity V. So we have,

16x2 + 4y+ 9z2 – 16xy + 12yz – 24zx = (4x)2 + (-2y)2 + (-3z)2 + 2(4x)(-2y) + 2(-2y)(-3z) + 2(-3z)(4x)= (4x – 2y – 3z)2 = (4x – 2y – 3z)(4x – 2y – 3z)

 

Example 4: Expand (3x – 4y)using standard algebraic identities.

Solution: (3x– 4y)is of the form Identity VII where a = 3x and b = 4y. So we have,

(3x – 4y)3 = (3x)3 – (4y)3– 3(3x)(4y)(3x – 4y) = 27x3 – 64y3 – 108x2y + 144xy2

 

Example 5: Factorize (x3 + 8y+ 27z3 – 18xyz) using standard algebraic identities.

Solution: (x3 + 8y+ 27z3 – 18xyz)is of the form Identity VIII where a = x, b = 2y and c = 3z. So we have,

(x3 + 8y+ 27z3 – 18xyz) = (x)3 + (2y)+ (3z)3 – 3(x)(2y)(3z)= (x + 2y + 3z)(x+ 4y2 + 9z2 – 2xy – 6yz – 3zx)



Frequently Asked Questions on Algebraic Identities

What are the three algebraic identities in Maths?

The three algebraic identities in Maths are:

Identity 1: (a+b)^2 = a^2 + b^2 + 2ab

Identity 2: (a-b)^2 = a^2 + b^2 – 2ab

Identity 3: a^2 – b^2 = (a+b) (a-b)

What is the difference between an algebraic expression and identities?

An algebraic expression is an expression which consists of variables and constants. In expressions, a variable can take any value. Thus, the expression value can change if the variable values are changed. But algebraic identity is equality which is true for all the values of the variables.

How to verify algebraic identity?

The algebraic identities are verified using the substitution method. In this method, substitute the values for the variables and perform the arithmetic operation. Another method to verify the algebraic identity is the activity method. In this method, you would need a prerequisite knowledge of Geometry and some materials are needed to prove the identity.








Monday, February 8, 2021

Computer test

Computer Test

Computer Test

 To give test, Click on:

Computer TEST

टेस्ट देने के लिए, इस पर क्लिक करें:




Computer Test 

Hello everyone. This is Mohit Sharma. I want to inform you that this is a practice test paper of Computer. First read all the guidelines then after that you can attempt this short quiz. Here a link is given to you at last. Click on the link and attempt this short quiz.

सभी को नमस्कार। मेरा नाम मोहित शर्मा है । मैं आपको सूचित करना चाहता हूं कि यह COMPUTER   का एक अभ्यास परीक्षण पेपर है। सभी दिशानिर्देशों को पढ़ें इसके बाद आप इस संक्षिप्त प्रश्नोत्तरी का प्रयास कर सकते हैं। यहां पर आपको आखिरी में एक लिंक दिया गया है। लिंक पर क्लिक करें और इस संक्षिप्त प्रश्नोत्तरी का प्रयास करें।
ALL THE BEST. ✌

Guidelines:
This is a quiz test. You have to attempt all questions.
Total Questions: 10
Max. marks: 10 (Each question carry 1 mark)
Subject: Computer
School: J.P. PUBLIC ACADEMY, KASGANJ

After attempting short quiz you will get your SCORE on screen with correct answers if you have done any question incorrect.

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