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Question
Divide x6 – y6 by the product of x2 + xy + y2 and x – y.
Solution
Product of (x2 + xy + y2) and (x − y)
= (x − y) (x2 + xy + y2)
= x(x2 + xy + y2) − y(x2 + xy + y2)
= x3 + x2y + xy2 − x2y − xy2 − y3
= x3 − y3
Now, (x6 − y6) ÷ (x3 − y3)
= x3 + y3
`"x"^3-"y"^3)overline("x"^6 -"y"^6)("x"^3+"y"^3`
x6 − x3y3
− +
x3y3 − y6
x3y3 − y6
− +
×
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