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
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HINT:
$$a^4+a^2b^2+b^4+a(a^3+b^3)$$
$$=(a^2-ab+b^2)(a^2+ab+b^2)+a(a+b)(a^2-ab+b^2)$$
answered Dec 22, 2015 at 5:09
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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
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$\begingroup$ @AdityaBidwai, Tried to utilize $a^4+a^2b^2+b^4$ $\endgroup$ Dec 22, 2015 at 5:12
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$\begingroup$ i am gonna put some more qs and im in emergency... pls do answer my questions $\endgroup$ Dec 22, 2015 at 5:13
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Hint : $(a^2+b^2)^2-a^2b^2=a^4+a^2b^2+b^4$
$$(a^2-a b+b^2) (2 a^2+2 a b+b^2)$$
answered Dec 22, 2015 at 5:07