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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 - RRB Technician Grade I Signal 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 expressions is the factor of $large 16x^2-4$ ?
A. 4x-2	B. 2x-2	C. 2-4x	D. 4-2x
Right Option : A
View Explanation

Question : 2

Factorize using identities : $-16x^{2}+64x^{4}$
A. $(1+8x^{2})^{2}$	B. $(8x^{2}-4x)(8x^{2}+4x)$	C. $(1-8x^{2})^2$	D. $(8x^{2}-4x)(8x^{2}+2x)$
Right Option : B
View Explanation

Question : 3

Factorise the following expression: $4x^2 - 8x + 4$
A. 2x - 2, 2x - 2	B. 2x + 2, 2x + 8	C. 2x - 2, 2x - 8	D. 2x - 2, 2x - 2
Right Option : D
View Explanation

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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 [20]

Cheshta

Archit Segal

Manish Kumar

Shreya Shrivastava

Upmanyu Sharma

Aman Kumar Shrivastava

Manya

Hiya Gupta

Om Umang

Anika Saxena

Aman Kumar Shrivastava

Sharandeep Singh

Aman Kumar Shrivastava

Barkha Arora

Ayan Ghosh

Hridey Preet

Ayan Ghosh

Barkha Arora

Yatharthi Sharma

Prisha Gupta

= $(4x)^{2}-(2^{2})$