Choose the correct answer from the alternatives given.
If 2x = a + 3. then find the value of $8 x^{3}$ - 18ax:

a^{3}

+ 27

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a^{3}

- 27

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a^{3}

+ 25

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a^{3}

- 36

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Solution

The correct option is A $a^{3}$ + 27
$2 x = a + 3$
$\Rightarrow$ $2 x - 3 = a$ ---- ( 1 )
$\Rightarrow$ $(2 x - 3)^{3} = a^{3}$
$\Rightarrow$ $8 x^{3} - 27 - 3 \times 2 x \times 3 \times (2 x - 3) = a^{3}$
$\Rightarrow$ $8 x^{3} - 27 - 18 x \times a = a^{3}$
$\Rightarrow$ $8 x^{3} = a^{3} + 18 a x + 27$
$\Rightarrow$ $8 x^{3} - 18 a x = a^{3} + 27$

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