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Factorisation Using Square Identities

Factorisation - Concepts

Factorization into Monomials

Factorization by Grouping of Terms

Factorisation Using Square Identities

Factorization by Middle Term Splitting

Class - 8th DAV 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

Which of the following identities should be used to factorize $large frac{x^2}{4}-frac{y^2}{25}$ ?
A. $a^2-b^2=(a-b)(a-b)$	B. $a^2+b^2=(a-b)(a+b)$	C. $a^2-b^2=(a-b)(a+b)$	D. None of the above
Right Option : C
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

Factorise using identities : $4p^{2}-20 pq+25q^{2}$
A. $(2p-5q)^{4}$	B. $(2p-5q)^{2}$	C. $(5p-2q)^{2}$	D. $(2p+5q)^{2}$
Right Option : B
View Explanation

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Language - English

Chapters

Exponents And Radicals II

Direct and Inverse Variation III

Construction of Quadriletrals

Understanding Quadriletrals II

Understanding Quadriletrals I

Linear Equations in One Variable II

Linear Equations in One Variable I

Cube and Cube Roots

Square and Square Root II

Square and Square Root I

Mensuration I

Exponents And Radicals I

Direct and Inverse Variation II

Direct and Inverse Variation I

Statistics and Probability I

Statistics and Probability II

Factorisation

Algebraic Identities

Polynomial

Simple and Compound Interest

Profit Loss and Discount

Percentages

Introduction to Graphs

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State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

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English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

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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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Manish Kumar

Aman Kumar Shrivastava

Manish Kumar

Sharandeep Singh

Yatharthi Sharma

Shreya Shrivastava

Aman Kumar Shrivastava

Barkha Arora

Manya

Shreya Shrivastava

Upmanyu Sharma

Ayan Ghosh

Ayan Ghosh

Barkha Arora

Prisha Gupta

Hiya Gupta

Shivam Rana

Cheshta

Yogansh Nyasi