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Difference of Two Squares

Factorise: ...

Question

Factorise: $27 x^{3} - 1331 y^{3}$

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Solution

$27 x^{3} - 1331 y^{3}$
$= {(3 x)}^{3} - {(11 y)}^{3}$
As we know that,
$a^{3} - b^{3} = (a - b) (a^{2} - a b + b^{2})$
Here, in the given expression,
$a = 3 x, b = 11 y$
$∴ 27 x^{3} - 1331 y^{3}$
$= {(3 x)}^{3} - {(11 y)}^{3}$
$= (3 x - 11 y) ({(3 x)}^{2} + (3 x) (11 y) + {(11 y)}^{2})$
$= (3 x - 11 y) (9 x^{2} + 33 x y + 121 y^{2})$
Thus $27 x^{3} - 1331 y^{3} = (3 x - 11 y) (9 x^{2} + 33 x y + 121 y^{2})$ .
Hence the correct answer is $(3 x - 11 y) (9 x^{2} + 33 x y + 121 y^{2})$ .

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Difference of Two Squares

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