Question

Exemplo: (a+b)³ = (a+b) . (a+b)² = (a+b) . (a²+2ab+b²) = a³ + 2a²b+ab²+ba²+2ab²+b³ = a³+3a²b+3ab²+b³

Efetue:

a) (x+2)³
b) (x-2)³
c) (5x+3y)³
d) (a-4b)³
e) (1-10x)³
f) (x+y)³

Answer 1

a) (x+2)³ =
   x³ +3.x².2+3.x.2²+2³
   x³ +6x²+12.x+8

b) (x-2)³
 x³ +3.x².(-2)+3.x.(-2)²+(-2)³
   x³ - 6x²+12.x - 8

c) (5x+3y)³
 (5x)³ + 3.(5x)².(3y)+3.(5x).(3y)² + (3y)³
   125x³ + 225x²y + 135xy² + 27y³

d) (a-4b)³
    a³ +3.a².(-4b)+3.a.(-4b)²+(-4b)³
   a³ - 12a²b + 48ab² - 64b³

e) (1-10x)³
    1³ +3.1².(-10x)+3.1.(-10x)²+(-10x)³
   1 - 30x + 300x² - 1000x³

f) (x+y)³
    x³ + 3.(x)².(y)+3.(x).(y)² + (y)³
       x³ + 3x²y + 3xy² + y³