Respuesta:
[tex](x + y)(x - y) {}^{2} =x {}^{3} - x {}^{2}y - xy {}^{2} + y {}^{3} [/tex]
Explicación paso a paso:
usando
[tex](x - y) {}^{2} = \alpha {}^{2} - 2 \alpha \beta + \beta {}^{2} [/tex]
Desarrolle la expresión
[tex](x + y) |(x - y) {}^{2} | \geqslant (x {}^{2} - 2xy + y {}^{2} )[/tex]
Multiplicar los paréntesis
[tex](x + y) \times (x {}^{2} - 2xy + y {) \geqslant }^{2} x {}^{3} - 2x {}^{2} y + xy {}^{2} + x {}^{2} y - 2xy {}^{2} + xy {}^{3} [/tex]
agrupe los términos semejantes
[tex]x {}^{3} ( | - 2x {}^{2}y)( | + xy {}^{2} |) + x {}^{2}y | - 2xy {}^{2} + y {}^{3} [/tex]
[tex] \geqslant x {}^{3} ( | - x {}^{2}y | ) + xy {}^{2} - 2xy {}^{2} + y {}^{3} [/tex]
[tex] \geqslant x {}^{3} - x {}^{2} y - xy {}^{2} + y {}^{3} [/tex]
