How do you factor $199 b^{3} - 133 b$ $199b^3-133b$ ?

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How do you factor $199 b^{3} - 133 b$ $199b^3-133b$ ?

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Answer 1 · 2016-06-03T08:13:30

$199 b^{3} - 133 b = b (\sqrt{199} b - \sqrt{133}) (\sqrt{199} b + \sqrt{133})$ $199b^3-133b=b(sqrt(199)b-sqrt(133))(sqrt(199)b+sqrt(133))$

Explanation:

The difference of squares identity can be written:

$A^{2} - B^{2} = (A - B) (A + B)$ $A^2-B^2 = (A-B)(A+B)$

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

$199 b^{3} - 133 b$ $199b^3-133b$

$= b (199 b^{2} - 133)$ $=b(199b^2-133)$

$= b ({(\sqrt{199} b)}^{2} - {(\sqrt{133})}^{2})$ $=b((sqrt(199)b)^2-(sqrt(133))^2)$

$= b (\sqrt{199} b - \sqrt{133}) (\sqrt{199} b + \sqrt{133})$ $=b(sqrt(199)b-sqrt(133))(sqrt(199)b+sqrt(133))$

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How do you factor $199 b^{3} - 133 b$ $199b^3-133b$ ?

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How do you factor $199 b^{3} - 133 b$ $199b^3-133b$ ?