Question

verify the identity (a+b)³ = a³+b³+3ab(a+b)
Solve please​

Answer 1

Answer:

(a-b)³=a³-3 a²b+3 ab²-b³

By transposition,

Answer 2

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(a + b)³ = a³ + b³ + 3ab(a + b)

(a + b)(a + b)(a + b) = a³ + b³ + 3ab(a + b)

(a(a + b) + b(a + b))(a + b) = a³ + b³ + 3ab(a + b)

(a² + ab + ab + b²)(a + b) = a³ + b³ + 3ab(a + b)

(a² + 2ab + b²)(a + b) = a³ + b³ + 3ab(a + b)

a(a² + 2ab + b²) + b(a² + 2ab + b²) = a³ + b³ + 3ab(a + b)

a³ + 2a²b + ab² + a²b + 2ab² + b³ = a³ + b³ + 3ab(a + b)

a³ + b³ + 3a²b + 3ab² = a³ + b³ + 3ab(a + b)

a³ + b³ + 3ab(a + b) = a³ + b³ + 3ab(a + b)

LHS = RHS

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Hope it's helpful to you