Question 1139340
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<pre>

a)  a^4 +a^2b^2 +b^4 = 


           add and subtract  a^2*b^2


    = (a^4 + 2a^2*b^2 + b^4) - a^2*b^2  = {{{(a^2 + b^2)^2}}} - {{{(ab)^2}}} = 


          apply the formula  {{{x^2}}} - {{{y^2}}} = (x+y)*(x-y)


    = {{{(a^2 + ab + b^2)*(a^2 - ab + b^2)}}}.     <U>ANSWER</U>
</pre>


Done; i.e. factored.



<pre>
b)  a^4 + 4b^4 = a^4 + (2b^2)^2 = 


           add and subtract  2*a^2*(2b^2)


    = (a^4 + 2*a^2*(2b^2) + 4b^4) - 2*a^2*(2b^2) = 


    = (a^2 + 2b^2)^2 - 4*a^2*b^2 = 


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


          apply the formula  {{{x^2}}} - {{{y^2}}} = (x+y)*(x-y)


   = (a^2 - 2ab + 2b^2)*(a^2 + 2ab + 2b^2).
</pre>


Done; i.e. factored.



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See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Advanced-factoring.lesson>Advanced factoring</A>

in this site.