DESENVOLVA AS SEGUINTES EXPRESSÕES: a) (a+ b) ³b) (b- c)³c) (2...

$(a + b) {}^{3} = (a + b) imes (a + b) imes (a + b) = ( {a}^{2} + ab + ab + {b}^{2} ) imes (a + b) = ( {a}^{2} + 2ab + {b}^{2} ) imes (a + b) {a}^{3} + {a}^{2} b + 2 {a}^{2} b + 2ab {}^{2} + ab {}^{2} + {b}^{3} = {a}^{3} + 3 {a}^{2} b + 3ab {}^{2} + {b}^{3}$

b)

$(b - c) {}^{3} = (b - c) imes (b - c) imes (b - c) = ({b }^{2} - bc - bc + {c}^{2} ) imes (b - c) = ( {b}^{2} - 2bc + {c}^{2} ) imes (b - c) = {b}^{3} - {b}^{2} c - 2 {b}^{2} c + 2bc {}^{2} + bc {}^{2} - {c}^{ 3} = {b}^{3} - 3 {b}^{2} c + 3bc {}^{2} - {c}^{3}$

c)

$(2a + 1) {}^{3} = (2a + 1) imes (2a + 1) imes (2a + 1) = (4 {a}^{2} + 2a + 2a + 1) imes (2a + 1) = (4 {a}^{2} + 4a + 1) imes (2a + 1) = 8 {a}^{3} + 4 {a}^{2} + 8 {a}^{2} + 4a + 2a + 1 = 8 {a}^{3} + 12 {a}^{2} + 6a + 1$

d)

$(1 - 2a) {}^{3} = (1 - 2a) imes (1 - 2a) imes (1 - 2a) = (1 - 2a - 2a + 4 {a}^{2} ) imes (1 - 2a) = (1 - 4a + 4 {a}^{2} ) imes (1 - 2a) = 1 - 2a - 4a + 8 {a}^{2} + 4 {a}^{2} - 8 {a}^{3} = - 8 {a}^{3} + 12 {a}^{2} - 6a + 1$

e)

$(2x + y) {}^{3} = (2x + y) imes (2x + y) imes (2x + y) = (4 {x}^{2} + 2xy + 2xy + {y}^{2} ) imes (2x + y) = (4 {x}^{2} + 4xy + {y}^{2} ) imes (2x + y) = 8 {x}^{3} + 4 {x}^{2} y + 8 {x}^{2} y + 4x {y}^{2} + 2x {y}^{2} + {y}^{3} = 8 {x}^{3} + 12 {x}^{2} y + 6x {y}^{2} + {y}^{3}$

f)

$(3y - 1) {}^{3} = (3y - 1) imes (3y - 1) imes (3y - 1) = (9 {y}^{2} - 3y - 3y + 1) imes (3y - 1) = (9 {y}^{2} - 6y + 1) imes (3y - 1) = 27 {y}^{3} - 9 {y}^{2} - 18 {y}^{2} + 6y + 3y - 1 = 27 {y}^{3} - 27 {y}^{2} + 9y - 1$

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DESENVOLVA AS SEGUINTES EXPRESSÕES: a) (a+ b) ³b) (b- c)³c) (2...

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