Question

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

• A. $a^3-b^3$
• B. $a^3+b^3$
• C. $a-b$
• D. $a+b$

Answer 1

The correct option is B

$a^3+b^3$

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

($a^2+ab+b^2$)($a-b$)

= $a^2(a-b)+ab(a-b)+b^2(a-b)$

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

= $a^3-b^3$

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