Question

factorize the (x+y) ³-(x-y) ³​

Answer 1

EXPLANATION.

Factorizes : (x + y)³ - (x - y)³.

As we know that,

Formula of :

⇒ (a - b)³ = a³ - 3a²b + 3ab² - b³.

⇒ (a + b)³ = a³ + 3a²b + 3ab² + b³.

Using this formula in the equation, we get.

⇒ (x³ + 3x²y + 3xy² + y³) - (x³ - 3x²y + 3xy² - y³).

⇒ x³ + 3x²y + 3xy² + y³ - x³ + 3x²y - 3xy² + y³.

⇒ 6x²y + 2y³.

⇒ 2y(3x² + y²).

                                                                                                               

MORE INFORMATION.

(1) (x + y)² = x² + y² + 2xy.

(2) (x - y)² = x² + y² - 2xy.

(3) (x² - y²) = (x + y)(x - y).

(4) (x² + y²) = (x + y)² - 2xy.

(5) (x³ + y³) = (x + y)(x² - xy + y²).

(6) (x³ - y³) = (x - y)(x² + xy + y²).

(7) (x + y)³ = x³ + 3x²y + 3xy² + y³.

(8) (x - y)³ = x³ - 3x²y + 3xy² - y³