# factorization of a fourth degree polynomial

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

HINT:

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

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

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

Hint : $(a^2+b^2)^2-a^2b^2=a^4+a^2b^2+b^4$

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

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