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)#