Divide:
$x^{7} - y^{7}$ by $x - y$

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Solution

Steps:
1) Multiply $x - y$ with $x^{6}$ , to get $x^{7}$ , Remainder $= x^{6} y - y^{7}$
2)Multiply $x - y$ with $x^{5} y$ to get $x^{6} y$ , Remainder $= x^{5} y^{2} - y^{7}$
The process will go until deg(Remainder)<deg(x-y)
Step 7)Multiply $x - y$ with $y^{6}$ to get, $x y^{6} - y^{7}$ , Remainder $= 0$

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