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

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

Svar:

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

Forklaring:

# "Given" (x + a) (x + b) (x + c) "ekspansionen er" #

# = X ^ 3 + (a + b + c) x ^ 2 + (ab + bc + ac) x + abc #

# "nu" (x + 3) ^ 3 = (x + 3) (x + 3) (x + 3) #

# "med" a = b = c = 3 #

#rArr (x + 3) ^ 3 #

# = X ^ 3 + (3 + 3 + 3) x ^ 2 + (9 + 9 + 9) x + (3xx3xx3xx3) #

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

Svar:

#COLOR (blå) (y = x ^ 3 + 9x ^ 2 + 27x + 27) #

Forklaring:

# Y = (x + 3) ^ 3 #

#COLOR (hvid) (……….) x + 3 #

#farve (hvid) (……) xx x + 3 #

#COLOR (hvid) (…………) overlinie (x ^ 2 + 3x) #

#COLOR (hvid) (…………..) + 3x + 9 #

#COLOR (hvid) (………..) overlinie (x ^ 2 + 6x + 9) #

#farve (hvid) (…….) xx x + 3 #

#COLOR (hvid) (………….) overlinie (x ^ 3 + 6x ^ 2 + 9x) #

#COLOR (hvid) (………………….) 3x ^ 2 + 18x + 27 #

#COLOR (hvid) (………….) overlinie (farve (blå) (x ^ 3 + 9x ^ 2 + 27x + 27) #