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Factorisation Using Square Identities

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

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 : 2

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 : 3

If $(x^2+3x+5)(x^2-3x+5)=m^2-n^2,$ then m and n is
A. $x^2+5$ , $x^2-3x$	B. $x^2+5$ , $3x$	C. $x^2+5$ , $5x$	D. $x^2+3x$ , $3x$
Right Option : B
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 [10]

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Shivam Rana

Ayan Ghosh

Cheshta

Shreya Shrivastava

Eshan Arora

Hiya Gupta

Archit Segal

Manish Kumar

Barkha Arora

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