Question

Factorizar 4m2 – 4m (n – m) + (n - m)2

Answer 1

Respuesta:

$=9m^2-6mn+n^2$

Explicación paso a paso:

$4m^2-4m\left(n-m\right)+\left(n-m\right)^2$

$\left(n-m\right)^2:\quad n^2-2nm+m^2$

$=4m^2-4m\left(n-m\right)+n^2-2nm+m^2$

$\mathrm{Expandir}\:-4m\left(n-m\right):\quad -4mn+4m^2$

$=4m^2-4mn+4m^2+n^2-2nm+m^2$

$\mathrm{Agrupar\:terminos\:semejantes}$

$=4m^2+4m^2+m^2-4mn-2mn+n^2$

$\mathrm{Sumar\:elementos\:similares:}\:4m^2+4m^2+m^2=9m^2$

$=9m^2-4mn-2mn+n^2$

$\mathrm{Sumar\:elementos\:similares:}\:-4mn-2mn=-6mn$

$=9m^2-6mn+n^2$