Question

Reducir la siguiente expresión: (x+2)(x^2+2x+4)\(x^2-2x+4)(x-2)+64

Answer 1

Respuesta:

x^3+4x^2+8x+8

Explicación paso a paso:

Answer 2

Recuerda que:

$(x + y)( {x}^{2} - xy + {y}^{2} ) = {x}^{3} + {y}^{3} \\ (x - y) ({x}^{2} + xy + {y}^{2} ) = {x}^{3} - {y}^{3}$

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

...

$= (x - 2)( {x}^{2} + 2x + {2}^{2} )(x + 2)( {x}^{2} - 2x + {2}^{2} ) + 64 \\ = ({x}^{3} - 8)( {x}^{3} + 8) + 64\\ = ({x}^{3} )^{2} - {8}^{2} + 64 \\ = {x}^{6} - 64 + 64 \\ = {x}^{6}$