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Factorisation Using Cubic 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 Cubic Identities

Factorization of Algebraic Expressions Expressible as a Perfect Cube:

In order to factorize algebraic expressions expressible as a perfect cube, we use the following expressions.

$large (i);a^{3}+3a^2b+3ab^2+b^{3}=(a+b)^{3}=(a+b)(a+b)(a+b)$

$large (ii);a^{3}-3a^2b+3ab^2+b^{3}=(a-b)^{3}=(a-b)(a-b)(a-b)$

Illustration: Factorise the following

$large (i);8x^3+36x^2y+54xy^2+27y^3$

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

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

Factorization of Algebraic Expressions using Conditional Identity:

In order to factorize algebraic expressions expressible as the following expressions.

$large ;a^{3}+b^3+c^3-3abc= (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$

Illustration: Factorise the following

$large 8x^3+y^3+27z^3-18xyz$

$large =(2x)^{3}+y^3+(3z)^3-3 times (2x)times (y) times (3z)$

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

$large =(2x+y+3z)(4x^2+y^2+9z^2-2xy- 3yz -6xz)$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

One of the factor of $a^{3}+8b^{2}-64c^{3}+24abc ;;is:$
A. a + 2b - 4c
B. a - 2b + 4c
C. a + 2b + 4c
D. a - 2b - 4c
Right Option : A
View Explanation

Question : 2

The factors of $8a^3+b^3-6ab+1: : are$
A. $(2a+b-1)(4a^2+b^2+1-3ab-2a)$
B. $(2a-b+1)(4a^2+b^2-4ab+1-2a+b)$
C. $(2a+b+1)(4a^2+b^2+1-2ab-b-2a)$
D. $(2a-1+b)(4a^2+1-4a-b-2ab)$
Right Option : C
View Explanation

Question : 3

$a^1^2-1$ can be factorised as :
A. $large =(a-1)(a^2+1-a)(a-1)(a^2+a+1)(a^2+1)(a^4+1-a^2)$
B. $large =(a +1)(a^2+1+a)(a-1)(a^2+a+1)(a^2+1)(a^4+1-a^2)$
C. $large =(a +1)(a^2+1+a)(a+1)(a^2+a+1)(a^2+1)(a^4+1-a^2)$
D. $large =(a +1)(a^2+1-a)(a-1)(a^2+a+1)(a^2+1)(a^4+1-a^2)$
Right Option : D
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 Cubic Identities

Factorisation Using Cubic Identities

Factorization of Algebraic Expressions Expressible as a Perfect Cube:

Factorization of Algebraic Expressions using Conditional Identity:

Students / Parents Reviews [10]

Manish Kumar

Om Umang

Archit Segal

Shreya Shrivastava

Hiya Gupta

Ayan Ghosh

Eshan Arora

Prisha Gupta

Cheshta

Aman Kumar Shrivastava