Find the quotient obtained when we divide $a^{6} - b^{6}$ by the product of $a^{2} + a b + b^{2}$ and $a - b$ . $[3 M a r k s]$

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Solution

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

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

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

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

= $a^{3} - b^{3}$ $[1.5 M a r k s]$

Now, we shall divide $a^{6} - b^{6}$ by product obtained, i.e. $a^{3} - b^{3}$

$[1.5 M a r k s]$

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