The result obtained when we multiply $a^{6} - b^{6}$ with the product of $a^{2} + a b + b^{2}$ and $a - b$ is

$a^{9} - a^{6} b^{3} - a^{3} b^{6} + b^{9}$

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$a^{7} - a^{6} b^{3} - a^{3} b^{6} + b^{9}$

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$a^{9} - a^{6} b^{4} - a^{3} b^{6} + b^{9}$

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$a^{9} - a^{6} b^{3} - a^{3} b^{7} + b^{9}$

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Solution

The correct option is A
$a^{9} - a^{6} b^{3} - a^{3} b^{6} + b^{9}$

We shall first find the product of $a^{2} + a b + b^{2}$ and $a - b$ .

( $a^{2} + a b + b^{2}$ )( $a - b$ )

= $a^{2} (a - b) + a b (a - b) + b^{2} (a - b)$

= $a^{3} - a^{2} b + a^{2} b - a b^{2} + b^{2} a - b^{3}$

= $a^{3} - b^{3}$

Now, we shall multiply $a^{6} - b^{6}$ with the product obtained, i.e. $a^{3} - b^{3}$ .

$(a^{6} - b^{6}) \times (a^{3} - b^{3})$

= $a^{6} (a^{3} - b^{3}) - b^{6} (a^{3} - b^{3})$

$= a^{9} - a^{6} b^{3} - a^{3} b^{6} + b^{9}$

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Similar questions

The quotient obtained when we divide $a^{6} - b^{6}$ by the product of $a^{2} + a b + b^{2}$ and $a - b$ .

If $A^{2} - B^{2} = x^{2} - \frac{1}{4} a n d A B = \frac{x}{2}$ . Find the value of $A^{6} + B^{6}$ .

(a^{2} - b^{2}) + \frac{a^{4} - b^{4}}{2!} + \frac{a^{6} - b^{6}}{3!} + . . .

\infty

a^{2} + b^{2} = c^{2}

a^{6} + b^{6} + 3 a^{2} b^{2} c^{2} = c^{6}

On Resolving $a^{6} - b^{6}$ into factors give $(a + b) (a - b) (a^{2} - a b + b^{2}) (a^{2} + a b + b^{2})$ .

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