De standaardvorm van y = (2x +3) ^ 3 - (4x-2) ^ 2?

De standaardvorm van y = (2x +3) ^ 3 - (4x-2) ^ 2?
Anonim

Antwoord:

#:. kleur (blauw) (y = 8x ^ 3 + 20x ^ 2 + 70x + 23 #

Uitleg:

# Y = (2x + 3) ^ 3- (4x-2) ^ 2 #

Eerst vereenvoudigen # (2x + 3) ^ 3 #

#color (wit) (AAAAAAAAAAAAA) ## 2x + 3 #

#color (wit) (aaaaaaaaaaa) ## onderstrepen (xx 2x + 3) #

#color (wit) (AAAAAAAAAAAAA) ## 4x ^ 2 + 6x #

#color (wit) (aaaaaaaaaaaaaaaaaaa) ## 6x + 9 #

#color (wit) (AAAAAAAAAAAAA) ##overline (4x ^ 2 + 12x + 9) #

#color (wit) (aaaaaaaaaaa) ## xx 2x + 3 #

#color (wit) (AAAAAAAAAAAAA) ##overline (8x ^ 3 + 2 + ^ 24x 18x) #

#color (wit) (aaaaaaaaaaaaaaaaaa) ## 12x ^ 2 + 36x + 27 #

#color (wit) (AAAAAAAAAAAAA) ##overline (kleur (paars) (8x ^ 3 + 36x ^ 2 + 54x + 27) #

Vereenvoudig dan #color (groen) ((4x-2) ^ 2 #

#color (groen) (= (4x-2) (4x-2)) #

#:. kleur (groen) ((4x-2) ^ 2 = 16x ^ 2-16x + 4 #

#color (paarse) ((2x + 3) = 8x ^ 3 ^ 3 + 36x ^ 2 + 54x + 27 #

#:. y = 8x ^ 3 + 36x ^ 2 + 54x + 27- (16x ^ 2-16x + 4) #

#:. kleur (oranje) (y = 8x ^ 3 + 36x ^ 2 + 54x + 27-16x ^ 2 + 16x-4) #

#:. kleur (blauw) (y = 8x ^ 3 + 20x ^ 2 + 70x + 23 #