Hvad er standardformen for y = (x +6) (x + 5) ^ 2 (x + 10) ^ 2?

Hvad er standardformen for y = (x +6) (x + 5) ^ 2 (x + 10) ^ 2?
Anonim

Svar:

# Y = x ^ 5 + 36x ^ 4 + 505x ^ 3 + 3450x ^ 2 + 11500x + 15000 #

Forklaring:

# Y = (x + 6) (x + 5) ^ 2 (x + 10) ^ 2 #

FOIL # (X + 5) ^ 2 #:

# Y = (x + 6) (x ^ 2 + 10x + 25) (x + 10) ^ 2 #

FOIL # (X + 10) ^ 2 #:

# Y = (x + 6) (x ^ 2 + 10x + 25) (x ^ 2 + 20x + 100) #

Fordel de to første sektioner inden for parentes:

#Y = (x + 6) (x ^ 2) + (x + 6) (10x) + (x + 6) (25) x ^ 2 + 20x + 100 #

Forenkle:

#Y = {(x ^ 2) (x) + (x ^ 2) (6) + (10x) (x) + (10x) (6) + (25) (x) + (25) (6)} x ^ 2 + 20x + 100 #

Forenkle yderligere:

# Y = (x ^ 3 + 6x ^ 2 + 10x ^ 2 + 60x + 25x + 150) (x ^ 2 + 20x + 100) #

Kombiner lignende udtryk inden for de første parenteser:

# Y = (x ^ 3 + 16x ^ 2 + 85X + 150) (x ^ 2 + 20x + 100) #

Distribuere:

#Y = (x ^ 2 + 20x + 100) (x ^ 3) + (x ^ 2 + 20x + 100) (16x ^ 2) + (x ^ 2 + 20x + 100) (85X) + (x ^ 2 + 20x + 100) (150) #

Fordel yderligere:

#Y = {(x ^ 3) (x ^ 2) + (x ^ 3) (20x) + (x ^ 3) (100)} + {(16x ^ 2) (x ^ 2) + (16x ^ 2) (20x) + (16x ^ 2) (100)} + {(85X) (x ^ 2) + (85X) (20x) + (85X) (100)} + {(150) (x ^ 2) + (150) (20x) + (150) (100)} #

Forenkle inden for parentes:

# Y = x ^ 5 + 20x ^ 4 + 100x ^ 3 + 16x ^ 4 + 320x ^ 3 + 1600x ^ 2 + 85X ^ 3 + 1700x ^ 2 + 8500x + 150x ^ 2 + 3000x + 15000 #

Kombiner lignende udtryk:

# Y = x ^ 5 + 36x ^ 4 + 505x ^ 3 + 3450x ^ 2 + 11500x + 15000 #