The correct option is B 27a^3 9a^2 + a 1/27 ( 3a 1/3 )^3 using the formula, (a + b)^3 = a^3 + b^3 + 3ab(a + b) =(3a)^3 +( 1/3)^3+3× ...

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Algebraic Identities

Expand 3a ...

Question

Expand ${(3 a - \frac{1}{3})}^{3}$

27 a^{3} - 9 a^{2} + a - \frac{1}{27}

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27 a^{3} - a^{2} + a - \frac{1}{27}

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27 a^{3} - a^{2} + a - \frac{1}{42}

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27 a^{3} - 9 a^{2} + a - \frac{1}{42}

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Solution

The correct option is B $27 a^{3} - 9 a^{2} + a - \frac{1}{27}$
${(3 a - \frac{1}{3})}^{3}$
using the formula, $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$= (3 a)^{3} + (- \frac{1}{3})^{3} + 3 \times (3 a) \times (- \frac{1}{3}) (3 a - \frac{1}{3})$
$= 27 a^{3} - 9 a^{2} + a - \frac{1}{27}$

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