How do you factor 199b^3-133b199b3133b?

1 Answer
Jun 3, 2016

199b^3-133b=b(sqrt(199)b-sqrt(133))(sqrt(199)b+sqrt(133))199b3133b=b(199b133)(199b+133)

Explanation:

The difference of squares identity can be written:

A^2-B^2 = (A-B)(A+B)A2B2=(AB)(A+B)

First note that 199b^3199b3 and 133b133b are both divisible by bb, so separate that out as a factor first...

199b^3-133b199b3133b

=b(199b^2-133)=b(199b2133)

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

=b(sqrt(199)b-sqrt(133))(sqrt(199)b+sqrt(133))=b(199b133)(199b+133)