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Factorisation Using Square Identities

Algebraic Identities - Concepts

Algebraic Identity - Square of Sum of Binomial

Algebraic Identity - Square of difference of Binomial

Algebraic Identity - Dfference of Square

Algebraic Identity -3

Algebraic Identity - Square of Trinomial

Algebraic Identity - Difference of Cubes

Algebraic Identity - Sum 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 - Quantitative Aptitude Proficiency 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 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

Question : 2

The factors of $a^2-1-2x-x^2$ are
A. $(a-x+1)(a-x-1)$		B. $(a+x-1)(a-x+1)$
C. $(a+x+1)(a-x-1)$		D. none of these
Right Option : C
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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Chapters

Problems On Boats And Stream

Rules For Divisibility

Square and Square Root

Profit Loss and Discount

Simple and Compound Interest

Ratio and Proportion

Partnership and Mixture

Time, Speed and Distance

Quadratic Equations

Time and Work

Mensuration

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Introduction to Trigonometry

Permutation and Combination

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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:

Students / Parents Reviews [10]

Yatharthi Sharma

Prisha Gupta

Barkha Arora

Cheshta

Hiya Gupta

Shreya Shrivastava

Om Umang

Archit Segal

Manish Kumar

Eshan Arora