The expanded form of $(3 x - 5)^{3}$ is
(a) $27 x^{3} + 135 x^{2} + 225 x - 125$
(b) $27 x^{3} + 135 x^{2} - 225 x - 125$
(c) $27 x^{3} - 135 x^{2} + 225 x - 125$
(d) none of these

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Solution

The correct option is (c) $27 x^{3} - 135 x^{2} + 225 x - 125$

We have
$(3 x - 5)^{3}$
$= 3 x^{3} - 5^{3} - 3 \times 3 x \times 5 (3 x - 5)$ [ $∵ (a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$ ]
$= 27 x^{3} - 125 - 45 x (3 x - 5)$
$= 27 x^{3} - 125 - 135 x^{2} + 225 x$
$= 27 x^{3} - 135 x^{2} + 225 x - 125$

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Factorize using Identity 27x³-135x²-225x-125.

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