If x + y = 1 + xy, then x3 + y3

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If x + y = 1 + xy, then x³ + y³ – x³y³ is equal to :

1. 0
2. 1
3. –1
4. 2

Correct Option: B

x + y = 1 + xy (given)
∴ x³ + y³ - x³.y³ = (x + y)³ – 3xy (x + y) – x³y³
x³ + y³ - x³.y³ = (1 + xy)³ – 3xy (1 + xy) – x³y³
x³ + y³ - x³.y³ = 1 + x³y³ + 3xy + 3x²y² - 3xy - 3x²y² - x³y³ = 1