The LCM of the expressions $x^{3} - a^{3}$ and $(x - a)^{2}$ is

(x^{3} - a^{3}) (x + a)

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(x^{3} - a^{3}) (x - a)^{2}

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(x - a)^{2} (x^{2} + a x + a^{2})

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(x + a)^{2} (x^{2} + a x + a^{2})

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Solution

The correct option is C $(x - a)^{2} (x^{2} + a x + a^{2})$
Let $f (x) = x^{3} - a^{3}$
$f (x) = (x - a) (x^{2} + a x + a^{2})$

Let $g (x) = (x - a)^{2}$
$g (x) = (x - a) (x - a)$

So, LCM
$\Rightarrow (x - a) (x^{2} + a x + a^{2}) (x - a)$

$\Rightarrow (x - a)^{2} (x^{2} + a x + a^{2})$

Hence, this is the answer.

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a_{1}

a_{2}

x^{3} - a^{3}

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\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

M & N

M P & N P

P

P

(1 + x) (1 + x + x^{2}) (1 + x + x^{2} + x^{3}) . . . . . . (1 + x + x^{2} + . . . . + x^{30}) = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . . . . + a_{465} x^{465}

a_{0} + a_{2} + a_{4} + . . . . . . . . + a_{464}

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