Question

resuelve el siguiente ejercicio (x+y) (x-y)²​

Answer 1

Respuesta:

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

Explicación paso a paso:

usando

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

Desarrolle la expresión

$(x + y) |(x - y) {}^{2} | \geqslant (x {}^{2} - 2xy + y {}^{2} )$

Multiplicar los paréntesis

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

agrupe los términos semejantes

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

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

$\geqslant x {}^{3} - x {}^{2} y - xy {}^{2} + y {}^{3}$