Divide: $x^{9} + y^{9}$ by $x^{3} + y^{3}$

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Solution

Steps for dividing $x^{9} + y^{9}$ by $x^{3} + y^{3}$ :
Step 1: Multiply $x^{3}$ with $x^{6}$ to get $x^{9}$ , Remainder= $- x^{6} y^{3} + y^{9}$
Step 2: Multiply $x^{3}$ with $- x^{3} y^{3}$ to get $- x^{6} y^{3}$ ,Remainder $= x^{3} y^{6} + y^{9}$
Step 3: Multiply $x^{3}$ with $y^{6}$ to get $x^{3} y^{6}$ , Remainder $= 0$

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