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# How do you factor completely 3x^3y - 48xy^3?

May 7, 2016

$3 x y \left(x - 4 y\right) \cdot \left(x + 4 y\right)$

#### Explanation:

$3 {x}^{3} y - 48 x {y}^{3}$

Taking 3xy common in the above expression, we get,
$3 x y \left({x}^{2} - 16 {y}^{2}\right)$
$= 3 x y \left({x}^{2} - {\left(4 y\right)}^{2}\right)$

Now, since
$\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \cdot \left(a + b\right)$

the above expression reduces to
$3 x y \left(x - 4 y\right) \cdot \left(x + 4 y\right)$

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