Question

Desenvolva as seguintes expressões
a)(2a+1)³
b)(1-2a)³

Answer 1

a)
= (2a + 1)³ 

= (2a + 1)².(2a + 1)

= (4a² + 2.2a + 1).(2a + 1 )

= (4a² + 4a + 1).(2a + 1)

= 4a².2a + 4a².1 + 4a.2a + 4a.1 + 1.2a + 1.1

= 8a³ + 4a² + 8a² + 4a + 2a + 1

= 8a³ + 12a² + 6a + 1
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b)

= (1 - 2a)³

= (1 - 2a)².(1 - 2a)

= (1 - 2.1.2a + 4a²) . ( 1 - 2a)

= (1 - 4a + 4a²).(1 - 2a)

= 1.1 + 1.(-2a) - 4a.1 - 4a.(-2a) + 4a².1 + 4a² . ( - 2a)

= 1 - 2a - 4a + 8a² + 4a²  - 8a³

= 1 - 6a + 12a² - 8a³

= - 8a³ + 12a² - 6a + 1
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