Factor a^4+2a^2b^2+9b^4

Math
a4+2a2b2+9b4
Rewrite the middle term.
a4+2a2(3b2)-4a2b2+9b4
Rearrange terms.
a4+2a2(3b2)+9b4-4a2b2
Factor first three terms by perfect square rule.
(a2+3b2)2-4a2b2
Rewrite 4a2b2 as (2ab)2.
(a2+3b2)2-(2ab)2
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a2+3b2 and b=2ab.
(a2+3b2+2ab)(a2+3b2-(2ab))
Simplify.
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Multiply 2 by -1.
(a2+3b2+2ab)(a2+3b2-2(ab))
Remove parentheses.
(a2+3b2+2ab)(a2+3b2-2ab)
(a2+3b2+2ab)(a2+3b2-2ab)
Factor a^4+2a^2b^2+9b^4

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