Question : Simplify: $(x+y)^3-(x-y)^3-6y(x^2-y^2)$
Option 1: $8y^3$
Option 2: $x^3$
Option 3: $8x^2$
Option 4: $y^3$
Correct Answer: $8y^3$
Solution : $(x+y)^3-(x-y)^3-6y(x^2-y^2)$ $=(x^3+3x^2y+3xy^2+y^3)-(x^3-3x^2y+3xy^2-y^3)-6x^2y+6y^3$ $=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-6x^2y+6y^3$ $=y^3+y^3+6y^3$ $=8y^3$ Hence, the correct answer is $8y^3$.
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