Question

Which of the following is a factor of (x + y)³ – (x³ + y³)?

Options

• x² + y² + 2xy

• x² + y² – xy

• xy²

• 3xy

Answer 1

3xy

Explanation:

Now,

(x + y)³ – (x³ + y³) = (x + y) – (x + y) (x² – xy + y²)     ...[Using identity, a³ + b³ = (a + b) (a² – ab + b²)]

= (x + y) [(x + y)² – (x² – xy + y²)]

= (x + y)(x² + y² + 2xy – x² + xy – y²)    ...[Using identity, (a + b)² = a² + b² + 2ab)]

= (x + y) (0 + 0 + 2xy – 0 + xy – 0)

= (x + y) (2xy + xy)

= (x + y) (3xy)

Hence, one of the factors of the given polynomial is 3xy.