Statement (A): ${(x - 3)}^{3} = x^{3} - 9 x^{2} + 27 x - 27$
Statement (B): ${(x + 2)}^{2} = x^{3} + 8 + 6 x^{2} + 12 x$

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Detailed Solution

Statement (A): ${(x - 3)}^{3} = x^{3} - 9 x^{2} + 27 x - 27$ $(∵ {(a - b)}^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3})$

Statement (B): ${(x + 2)}^{3} = x^{3} + 3. x^{2} .2 + 3. x {.2}^{2} + 2^{3}$

$= x^{3} + 6 x^{2} + 12 x + 8$ $(∵ {(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3})$

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