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Factorisation Using Square Identities

Polynomials III - Concepts

Factorization of Cubic Polynomial

Algebraic Identity - Sum of Cubes

Algebraic Identity - Difference of Cubes

Algebraic Identity -Cube of Sum of Binomial

Algebraic Identity -Cube of Difference of Binomial

Algebraic Identity- Conditional

Factorisation Using Square Identities

Factorisation Using Cubic Identities

Class - 9th IMO Subjects

Concept Explanation

Factorisation Using Square Identities

Factorisation Using the Difference of the Squares:

To factorize binomial expressions expressible as the difference of two squares, we use the following identity:

$a^{2}-b^{2}=(a+b)(a-b)$

Illustration: Factorise the following

$(i);x^{4}-y^{4}$ $=(x^{2})^{2}-(y^{2})^{2}$

$=(x^{2}-y^{2})(x^{2}+y^{2})$ $[Using:;;a^{2}-b^{2}=(a-b)(a+b)]$

$=(x-y)(x+y)(x^{2}+y^{2})$ $[Using:;;a^{2}-b^{2}=(a-b)(a+b)]$

$large (ii);x^{4}-(y+z)^{4}$ $=(x^{2})^{2}-left { (y+z)^{2} right }^{2}$

$large =left { x^{2}-(y+z)^{2} right }left { x^{2}+(y+z)^{2} right }$

$large =left { x-(y+z) right }left { x+(y+z) right }left { x^{2}+(y+z)^{2} right }$

$large (iii);2x-32x^{5}$ $large =2x(1-16x^{4})$

$large =2xleft { 1^{2}-(4x^{2})^{2} right }$

$large =2x(1+4x^{2})(1-4x^{2})$

$large =2x(1+4x^{2})left { 1-(2x)^{2} right }$

$large =2x(1+4x^{2})(1-2x)(1+2x)$

Factorization Using Perfect Square Identities:

In order to factorize algebraic expressions expressible as a perfect square, we use yhr following expressions.

$(i);a^{2}+2ab+b^{2}=(a+b)^{2}=(a+b)(a+b)$

$(ii);a^{2}-2ab+b^{2}=(a-b)^{2}=(a-b)(a-b)$

Illustration: Factorise the following

$(i);4x^{2}+12xy+9y^{2}$ $=(2x)^{2}+2times 2xtimes 3y+(3y)^{2}$

$=(2x+3y)^{2}$

$=(2x+3y)(2x+3y)$

$(ii);x^{4}+10x^{2}y^{2}+25y^{4}$ $=(x^{2})^{2}-2times x^{2}times 5y^{2}+(5y^{2})^{2}$

$=(x^{2}-5y^{2})^{2}$

$=(x^{2}-5y^{2})(x^{2}-5y^{2})$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The expression $x^4+4$ can be factorized as
A. $(x^2+2x+2)(x^2-2x+2)$		B. $(x^2+2x+2)(x^2+2x-2)$
C. $(x^2-2x-2)(x^2-2x+2)$		D. $(x^2+2)(x^2-2)$
Right Option : A
View Explanation

Question : 2

$large Factorise: ;2x-32x^{5}$
A. $large 2x(1+4x^{2})(1-2x)(1+2x)$		B. $large 2x(1+4x^{2})(1-2x)(2+x)$
C. $large 2x(1+4x^{2})(1-2x)(1+2x)$		D. $large x(1+4x^{2})(1-2x)(1+2x)$
Right Option : C
View Explanation

Question : 3

The number of factors of $(x^{9}-x)$ is :
A. 5	B. 4	C. 2	D. cannot be determined
Right Option : A
View Explanation

Video Link - Have a look !!!

Language - English

Chapters

Polynomials II

Direct and Inverse Variation

Linear Equations in One Variable

Introduction to Trigonometry

Introduction to Euclids Geometry

Herons Formula Complete

Polynomial I

Surface Area and Volume II

Surface Area and Volume I

Coordinate Geometry

Constructions

Areas Of Parallelograms And Triangles II

Areas Of Parallelograms And Triangles I

Linear Equations in Two Variables

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Attention !!!!!

Factorisation Using Square Identities

Factorisation Using Square Identities

Factorisation Using the Difference of the Squares:

Factorization Using Perfect Square Identities:

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Archit Segal

Ayan Ghosh

Shivam Rana

Prisha Gupta

Upmanyu Sharma

Cheshta

Hiya Gupta

Om Umang

Yatharthi Sharma

Hridey Preet

Manish Kumar

Sharandeep Singh

Anika Saxena

Yogansh Nyasi

Aman Kumar Shrivastava

Barkha Arora

Aman Kumar Shrivastava

Ayan Ghosh

Aman Kumar Shrivastava

Manish Kumar