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

1. x² + xy + 2xy

2. x² + y² - xy

3. xy²

4. 3xy

If $\dfrac{x}{y} + \dfrac{y}{x}$ = -1 (x ≠ 0, y ≠ 0), then the value of x³ - y³ is

1. 1

2. -1

3. 0

4. $\dfrac{1}{2}$

If $x^\frac{1}{3} + y^\frac{1}{3} + z^\frac{1}{3}$ = 0, then

1. x³ + y³ + z³ = 0

2. x³ + y³ + z³ = 27xyz

3. (x + y + z)³ = 27xyz

4. x + y + z = 3xyz

Consider the following two statements.

Statement 1: The factorisation of x² + 2x + 1 is (x - 1)².

Statement 2: (a - b)² = a² + 2ab + b².

Which of the following is valid?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and Statement 2 is false.

4. Statement 1 is false, and Statement 2 is true.