Hvad er standardformen for y = (x - 3) ^ 3?

Hvad er standardformen for y = (x - 3) ^ 3?
Anonim

Svar:

I standardformular # Y = x ^ 3-9x ^ 2 + 27x-27 #

Forklaring:

I # Y = (x-3) ^ 3 #, RHS er et polynom af grad #3# i #x#.

Standardformularen af et polynom i grad #3# er # Ax ^ 3 + bx ^ 2 + cx + d #, så vi skal bruge # (X-3) ^ 3 # ved at gange.

# (X-3) ^ 3 = (x-3) (x-3) ^ 2 #

= # (X-3) (x (x-3) -3 (x-3)) #

= # (X-3) (x ^ 2-3x-3x + 9) #

= # (X-3) (x ^ 2-6x + 9) #

= #x (x ^ 2-6x + 9) -3 (x ^ 2-6x + 9) #

= # X ^ 3-6 gange ^ 2 + 9x-3x ^ 2 + 18x-27 #

= # X ^ 3-9x ^ 2 + 27x-27 #