d Factorize 9 x 4 + 36y 4 of such expressions is done

Question 1: Factorize 9 x 4 + 36y 4



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

Factorizing an expression




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}


=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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