d Factorize 3 x 4 + 12y 4 to factorize this expression
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Question 3: Factorize 3 x 4 + 12y 4

a 4 + a 2 b 2 + b 4 or a 4 + 4b 4 type expressions 0

Question 3: Factorize 3 x 4 + 12y 4

Factorization is easy –

Solution :

 

Given expression is ;

3 x^{4}+12 y^{4}

Taking 3 common;

=3[x^4+4y^4]

This can be written as;

=3[(x^2)^2+(2y^2)^2]

Adding and subtracting 2x^2y^2

=3[(x^2)^2+(2y^2)^2+2(x^2)(2y^2)-2(x^2)(2y^2)]

First three terms in the bracket becomes whole square;

=3[(x^2+2y^2)^2-2(x^2)(2y^2)]

Re-wrting like;

=3[(x^2+2y^2)^2-4(x^2)(y^2)]

Taking both terms in the bracket as separate whole squares;

=3[(x^2+2y^2)^2-(2xy)^2]

This is now a^2-b^2 form – and can be written as;

=3[(x^2+2y^2+2xy)(x^2+2y^2-2xy)]

 

 



 


 

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