How do you factor #199b^3-133b#?

1 Answer
George C.
Jun 3, 2016

#199b^3-133b=b(sqrt(199)b-sqrt(133))(sqrt(199)b+sqrt(133))#

Explanation:

The difference of squares identity can be written:

#A^2-B^2 = (A-B)(A+B)#

First note that #199b^3# and #133b# are both divisible by #b#, so separate that out as a factor first...

#199b^3-133b#

#=b(199b^2-133)#

#=b((sqrt(199)b)^2-(sqrt(133))^2)#

#=b(sqrt(199)b-sqrt(133))(sqrt(199)b+sqrt(133))#

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