Care este forma standard a y = (5x + 3) ^ 3 + (7x-13) ^ 2?

Răspuns:

# (5x + 3) ^ 3 + (7x-13) ^ 2 = 125x ^ 3 + 274x ^ 2-47x +

Explicaţie:

În general, avem:

# (a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2 #

# (a + b) ^ 3 = a ^ 3 + 3a ^ 2b + 3ab ^ 2 + b ^ 3 #

Asa de:

(7x-13) ^ 2 = (7x) ^ 2-2 (7x) (13) + 13 ^ 2 #

#color (alb) ((7x-13) ^ 2) = 49x ^ 2-182x + 169 #

# (5x + 3) 3 = (5x) ^ 3 + 3 (5x) ^ 2 (3) +3 (5x)

#color (alb) ((5x + 3) ^ 3) = 125x ^ 3 + 225x ^ 2 + 135x + 27 #

Asa de:

# (5x + 3) ^ 3 + (7x-13) ^ 2 #

# = 125x ^ 3 + 225x ^ 2 + 135x + 27 + 49x ^ 2-182x + 169 #

# = 125x ^ 3 + (225 + 49) x ^ 2 + (135-182) x + (27 + 169)

# = 125x ^ 3 + 274x ^ 2-47x + 196 #