Question

Calculati: (28 a la n+2 -56 a la n+1 -84a la n) : (-7 a la n-1) ...Va rog

Answer 1

$N= \frac{28* a^{n+2}-56* a^{n+1}-84*a^{n}}{-7*a^{n-1}}$⇔
$N=\frac{7*(4* a^{(n-1)+3}-8*a^{(n-1)+2}-12*a^{(n-1)+1})}{-7*a^{n-1}}$⇔
$N=\frac{7*(4* a^{(n-1)}* a^{3} -8*a^{(n-1)}* a^{2} -12*a^{(n-1)}* a^{1} )}{-7*a^{n-1}}$⇔
$N=-\frac{(7*a^{(n-1)})*(4* a^{3} -8* a^{2} -12* a)}{(7*a^{n-1})}$
Fractia de mai sus se poate simplifica cu: $\\ 7*a^{(n-1)}$ si obtinem:
$N=(-1)*(4*a^{3} -8*a^{2} -12*a)$⇔$\\N=(-4)*(a^{3} -2a^{2} -3a)$⇔
$N=(-4)*a*( a^{2} -2a-3)=(-4a)*[ (a^{2}-1)-2a-2]$⇔
$N=(-4a)*[(a-1)*(a+1)-2*(a+1)]$$=(-4a)*[(a+1)*(a-1-2)]$
In final avem ca:   $N=(-4)*a*(a+1)*(a-3)$

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