Question

Rút gọn các biểu thức sau:

a) ( a + b )³ - ( a - b )^{3 -} 6a²b

b) ( a + b)³ + ( a - b )³ - 6ab²

Answer 1

a) \(\left(a+b\right)^3-\left(a-b\right)^3-6a^2b\)

\(=\left(a^3+3a^2b+3ab^2+b^3\right)-\left(a^3-3a^2b+3ab^2-b^3\right)-6a^2b\)

\(=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-6a^2b\)

\(=2b^3\)

b) \(\left(a+b\right)^3+\left(a-b\right)^3-6ab^2\)

\(=\left(a^3+3a^2b+3ab^2+b^3\right)+\left(a^3-3a^2b+3ab^2-b^3\right)-6ab^2\)

\(=a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3-6ab^2\)

\(=2a^3\)

Answer 2

a) ( a + b )³ - ( a - b )³ - 6a²b

<=> a³ + 3a²b + 3ab² + b³ - a³ + 3a²b - 3ab² + b³ - 6a²b

<=> 2b³

b) ( a + b)³ + ( a - b )³ - 6ab²

<=> a³ + 3a²b + 3ab² + b³ + a³ - 3a²b + 3ab² - b³ - 6a²b

<=> 2a³ - 6a²b + 6ab²

Answer 3

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