Arătați ca (x+6)^3-x-6=(x+5)(x+6)(x+7)

Vom da factor comun, apoi vom aplica formula diferenței de pătrate:

[tex](x+6)^3-(x+6) =(x+6) \cdot \Big[(x+6)^2-1^2\Big]=\\[/tex]

[tex]= (x+6) \cdot \Big[(x+6)-1\Big] \cdot \Big[(x+6)+1\Big][/tex]

[tex]= (x+6) \cdot (x+6-1) \cdot (x+6+1)[/tex]

[tex]= (x+5)(x+6)(x+7)[/tex]

Putem porni si invers:

(x+5)(x+6)(x+7)=(x+6)×(x+5)(x+7)=

(x+6)(x+6-1)(x+6+1)= (x+6)[(x+6)²-1]=

(x+6)³-(x+6)=(x+6)³-x-6.

Aici am folosit formula (a-b)(a+b)=a²-b².