Question

Rezolva exercitiul ca produs de 3 factori

x(-x+1)3-x(-x+1)2-x(x-1) , 3 si 2 sunt puteri

Answer 1

Răspuns:

Vezi atasament

Answer 2

$x {( - x + 1)}^{3} - x {( - x + 1)}^{2} - x(x - 1)$

$= x{[ - (x - 1)]}^{3} - x{[ - (x - 1)]}^{2} - x(x - 1)$

$= x \times {( - 1)}^{3} \times {(x - 1)}^{3} - x \times {( - 1)}^{2} \times {(x - 1)}^{2} - x(x - 1)$

$= x \times ( - 1) \times {(x - 1)}^{3} - x \times 1 \times {(x - 1)}^{2} - x(x - 1)$

$= - x {(x - 1)}^{3} - x {(x - 1)}^{2} - x(x - 1)$

$= -x(x - 1)[ {(x - 1)}^{2} + (x - 1) +1]$

$= -x(x - 1)[{x}^{2} - 2x + 1+x-1 +1]$

$= -x(x + 1)( {x}^{2} - x+1)$