Question

Factorise
${x}^{3} - 9 {y}^{3} - 3xy(x - y)$
​

Answer 1

Answer:

Given :-

➪ x³ - 9y³ - 3xy(x - y)

Solution :-

➪ x³ - 9y³ - 3xy(x - y)

➭ x³ - 9y³ - 3x²y + 3xy²

➭ x³ - 3x²y + 3xy² - 9y³

➭ x³ - 3x²y + 3xy² - y³ - 8y³

➭ (x - y)³ - (2y)³

➭ (x - y - 2y) {(x - y)² + (x - y) × 2y + (2y)²}

➭ (x - 3y) {(x)² - 2 × x × y + (y)² + 2xy - 2y² + 4y²}

➭ (x - 3y) (x² - 2xy + y² + 2xy - 2y² + 4y²)

➭ (x - 3y) (x² - 2xy + 2xy + y² - 2y² + 4y²)

➭ (x - 3y) (x² - y² + 4y²)

➭ (x - 3y) (x² + 3y²)

The value of x³ - 9y³ - 3xy(x - y) is

(x - 3y) (x² + 3y²)

Formula used :-

➪ (a - b)²

➭ a² - 2ab + b²

➪ (a - b)³

➭ a³ - 3a²b + 3ab² - b³

➪ a³ - b³

➭ (a - b) (a² + ab + b²)