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Question1: Factorize 81 x 4 + 36 x 2 y 2 + 16y 4

 

 

Question1: Factorize 81 x 4 + 36 x 2 y 2 + 16y 4

Factorization Questions

Solution:

The given expression is ;

81 x^{4}+36 x^{2} y^{2}+16 y^{4}

 =(9x ^{2})^{2}+72 x^{2} y^{2}+  (4y^{2})^{2}-36 x^{2}y ^{2}

Here first part is  (9x ^{2})^{2}+72 x^{2} y^{2}+  (4y^{2})^{2} while second part is  36 x^{2}y ^{2}. First part can be converted into  a^{2}+2(a)(b)+ b^{2} form as  (9x ^{2})^{2}+2(9 x^{2})( 4y^{2})+  (4y^{2})^{2}-36 x^{2}y ^{2}

So the given expression becomes;

= (9 x^{2}+4y ^{2})^{2}- (6xy)^{2}

Now this is in  a^{2}- b^{2} form;

So the factorization of given expression is ;

= (9 x^{2}+y ^{2}- 6xy) (9 x^{2}+y ^{2}+ 6xy)

 

 


 

 

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