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Question 4: Factorize a 4 + 3a 2 b 2 + 4b 4

 

Question 4: Factorize   a^4+3a^2b^2+4b^4

Factorization rules —

Solution:

 

Given expression is ;

a^4+3a^2b^2+4b^4

This can be written as;

=a^4+3a^2b^2+4b^4 +a^2b^2-a^2b^2  (adding and subtracting a^2b^2 )

=a^4+4a^2b^2+4b^4 -a^2b^2

Arranging to form a^2+2(a)(b)+b^2 form for first three terms;

=(a^2)^2+2(a^2)(2b^2)+(2b^2)^2-a^2b^2

Taking (a+b)^2 form for fist three terms in this way;

=(a^2+2b^2)^2 -a^2b^2

=[(a^2+2b^2)^2 -a^2b^2 ]

This is now a^2-b^2 form- writing in brackets;

=[(a^2+2b^2)^2 -(ab)^2 ]

Applying (a+b)(a-b) form;

=[(a^2+2b^2)+ab ] [(a^2+2b^2)-ab ]

=[a^2+2b^2+ab ] [a^2+2b^2-ab ]

 

 

 

 


 

 

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