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What could be the possible factorization of $$2a^4+a^2b^2+ab^3+b^4$$? what term should be added

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2 Answers 2

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HINT:

$$a^4+a^2b^2+b^4+a(a^3+b^3)$$

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

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  • $\begingroup$ sir how did it come to your mind to factorize this way? please may i know your thinking process $\endgroup$ Dec 22, 2015 at 5:11
  • $\begingroup$ @AdityaBidwai, Tried to utilize $a^4+a^2b^2+b^4$ $\endgroup$ Dec 22, 2015 at 5:12
  • $\begingroup$ sir you are fabulous... $\endgroup$ Dec 22, 2015 at 5:13
  • $\begingroup$ i am gonna put some more qs and im in emergency... pls do answer my questions $\endgroup$ Dec 22, 2015 at 5:13
  • $\begingroup$ thank you sir aditya bidwai $\endgroup$ Dec 22, 2015 at 5:14
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Hint : $(a^2+b^2)^2-a^2b^2=a^4+a^2b^2+b^4$

$$(a^2-a b+b^2) (2 a^2+2 a b+b^2)$$

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  • $\begingroup$ but sir how did you arrive at it? $\endgroup$ Dec 22, 2015 at 5:08
  • $\begingroup$ Factorize $a^4+ab^3$ $\endgroup$ Dec 22, 2015 at 5:11

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