Question

Como fazer cubo da soma e resolver essas contas? 25 pts


a) (x +3)³=
b) (2b+2)³ =
c) (x-3)³

Answer 1

a)
= (x + 3)³
= (x + 3)².(x + 3)
= (x² + 2.3x + 3²).(x + 3)
= (x² + 6x + 9).(x + 3)
= x².x + 3.x² + 6x.x + 3.6x + 9.x + 9.3
= x³ + 3x² + 6x² + 18x + 9x + 27
= x³ + 9x² + 27x + 27

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b)
= (2b + 2)³
= (2b + 2)².(2b + 2)
= (4b² + 2.2.2b + 4).(2b + 2)
= (4b² + 8b + 4).(2b + 2)
= 4b².2b + 4b².2 + 8b.2b + 2.8b + 4.2b + 4.2
= 8b³ + 8b² + 16b² + 16b + 8b + 8
= 8b³ + 24b² + 24b + 8

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c)
= (x - 3)³
= (x - 3)².(x - 3)
= (x² - 2.3x + 3²).(x - 3)
= (x² - 6x + 9).(x - 3)
= x².x - 3.x² - 6x.x - 3.(-6x) + 9.x + 9.(-3)
= x³ - 3x² - 6x² + 18x + 9x - 27
= x³ - 9x² + 27x - 27