Divide: $a^{4} + 4 b^{4}$ by $a^{2} + 2 a b + b^{2}$

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Solution

Steps:
1)Multiply $(a^{2} + 2 a b + b^{2})$ with $a^{2}$ , to get $a^{4}$ , Remainder $= - 2 a^{3} b - a^{2} b^{2} + 4 b^{4}$
2) Multiply $(a^{2} + 2 a b + b^{2})$ with $- 2 a b$ , to get $- 2 a^{3} b$ , Remainder $= 3 a^{2} b^{2} + 2 a b^{3} + 4 b^{4}$
3) Multiply $(a^{2} + 2 a b + b^{2})$ with $3 b^{2}$ , to get $3 a^{2} b^{2}$ , remainder $= - 4 a b^{3} + b^{4}$

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