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Question 1: Factorize 9 x 4 + 36y 4

 

 

Question 1: Factorize 9 x^{4}+36 y^{4}

Factorizing an expression

Solution:

 

 

Given expression is

9 x^{4}+36 y^{4}

Adding and subtracting 36x2y2  – into the expression;

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

or

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

Now first three terms can be re-written to take a form of a ^{2}+2 ab+ b^{2} as

=(3x^{2}) ^{2}+2(3x^{2})(6y^{2})+ (6y^{2})^{2} -36 x^{2}y^{2}

= (3 x^{2}+6 y^{2})^{2}-36 x^{2}y^{2}

= (3 x^{2}+6 y^{2})^{2}- (6 xy)^{2}

 

Now this is in   a^{2}-b ^{2} = (a-b)(a+b) form, so we get;

= (3 x^{2}+6 y^{2}- 6 xy)(3 x^{2}+6 y^{2}+ 6 xy)

 

 

 

 


 

 

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