Solve : $3 x^{3} y - 243 x y^{3}$

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Solution

$3 x^{3} y - 243 x y^{3}$

$\Rightarrow$ $3. (x)^{3} . y - 3^{5} . x y^{3}$

$\Rightarrow$ $3 x^{3} y - 3^{5} x y^{3}$

$\Rightarrow$ $3 x y (x^{2} - 81 y^{2})$

Factorizing $x^{2} - 81 y^{2}$

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

$= 3 x y (x + 9 y) (x - 9 y)$

$∴ 3 x^{3} y - 243 x y^{3} = 3 x y (x + 9 y) (x - 9 y)$ .

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