How do you factor $4a^4 + 6a^3b^2 + 2a^2b^3$ ?

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Answer 1 · 2016-08-28T20:55:00

$4a^4+6a^3b^2+2a^2b^3=2a^2(2a^2+3ab^2+b^3)$

$4a^4b+6a^3b^2+2a^2b^3=2a^2b(2a+b)(a+b)$

$4a^4+6a^3b^2+2a^2b^4=2a^2(2a+b^2)(a+b^2)$

If the expression is correct as given then we find:

$4a^4+6a^3b^2+2a^2b^3=2a^2(2a^2+3ab^2+b^3)$

with no further simplification.

If the first term was supposed to be $4a^4b$ then we find:

$4a^4b+6a^3b^2+2a^2b^3$

$=2a^2b(2a^2+3ab+b^2)$

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

If instead the last term was supposed to be $2a^2b^4$ then we find:

$4a^4+6a^3b^2+2a^2b^4$

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

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

How do you factor 4a^4 + 6a^3b^2 + 2a^2b^34a^4 + 6a^3b^2 + 2a^2b^3?