Factorise $18 x^{3} y^{3} - 27 x^{2} y^{3} + 36 x^{3} y^{2}$ .

9 x^{2} y^{2} (2 x y - 3 y + 4 x)

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9 x^{2} y^{2} (2 x y + 3 y + 4 x)

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9 x^{2} y^{2} (2 x y - 3 y - 4 x)

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9 x^{2} y^{2} (2 x y + 3 y - 4 x)

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Solution

The correct option is A $9 x^{2} y^{2} (2 x y - 3 y + 4 x)$
$18 x^{3} y^{3} - 27 x^{2} y^{3} + 36 x^{3} y^{2}$
$18 x^{3} y^{3}$
= $2 \times 3 \times 3 \times x \times x \times x \times y \times y \times y$

$27 x^{2} y^{3}$
= $3 \times 3 \times 3 \times x \times x \times y \times y \times y$

$36 x^{3} y^{2}$
= $2 \times 2 \times 3 \times 3 \times x \times x \times x \times y \times y$

$C o m m o n f a c t o r s a r e 3^{2}, x^{2} a n d y^{2}$

$18 x^{3} y^{3} - 27 x^{2} y^{3} + 36 x^{3} y^{2}$
$= 9 x^{2} y^{2} (2 x y - 3 y + 4 x)$

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