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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 CBSE 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

Factorise: $large ;3a^{4}-48b^{4}$
A. $large (a-2b)(a+2b)(a^{2}+4b^{2})$
B. $large 3(2a-b)(a+2b)(a^{2}+4b^{2})$
C. $large 3(a-2b)(a+2b)(a^{2}-4b^{2})$
D. $large 3(a-2b)(a+2b)(a^{2}+4b^{2})$
Right Option : D
View Explanation

Question : 2

Which of the following expression is a factor of $large 121y^2-36$ ?
A. 11y+6	B. 12y+9	C. 12y+6	D. 11y+1
Right Option : A
View Explanation

Question : 3

Which of the following expression is a factor of $large 49x^2-196$ ?
A. 8x+14	B. 6x+14	C. 7x+14	D. None of the above
Right Option : C
View Explanation

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Language - English

Chapters

Polynomials II

Linear Equations in One Variable

Introduction to Euclids Geometry

Herons Formula Complete

Polynomial I

Surface Area and Volume II

Surface Area and Volume I

Coordinate Geometry

Areas Of Parallelograms And Triangles II

Areas Of Parallelograms And Triangles I

Linear Equations in Two Variables

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