Question

(x+y)^9(x-y)^5-(x²-y²)^7≈

Answer 1

Resolver.


(x + y)⁹(x - y)⁵ - (x² - y²)⁷ =    Aplicas a² - b² = (a + b)(a - b)
(x + y)⁹(x - y)⁵ - ((x+ y)(x - y))⁷ =    Aplicas (a . b)ⁿ = aⁿ . bⁿ
(x + y)⁹(x - y)⁵ - [ (x + y)⁷(x - y)⁷]  =  Factorizas  Sacas factor comun
                                                     (x + y)⁷ y (x -y)⁵
(x + y)⁷(x - y)⁵ [(x + y)² - (x - y)²] =  Aplicas (a + b)² = a² + 2ab + b²
(x + y)⁷(x - y)⁵ [x² + 2xy + y² - (x² - 2xy + y²)] =
(x + y)⁷(x - y)⁵[ x² + 2xy + y² - x² + 2xy - y²] =
(x - y)⁷(x - y)⁵( 4xy)

Respuesta.
(x + y)⁷(x - y)⁵(4xy)