Question

Desenvolva cada um dos binômio de Newton a seguir.

Answer 1

Olá!



$a)(x + 3)^{4} \\ \\ (x + 3)^{2 + 2} \\ (x + 3)^{2} \times (x + 3)^{2} \\ ( {x}^{2} + 6x + 9) \times ( {x}^{2} + 6x + 9) \\ {x}^{4} + {6x}^{3} + {9x}^{2} + {6x}^{3} + {36x}^{2} + 54x + {9x}^{2} + 54x + 81 \\ \\ resposta : {x}^{4} + {12x}^{3} + {54x}^{2} + 108x + 81$




$b) ({2y - 1)}^{5} \\ \\ (2y - 1)^{3 + 2} \\ (2y - 1)^{3} \times (2y - 1)^{2} \\ ({8y}^{3} - {12y}^{2} + 6y - 1) \times ( {4y}^{2} - 4y + 1) \\ {32y}^{5} - {32y}^{4} + {8y}^{3} - {48y}^{4} + {48y}^{4} - {12y}^{2} + {24y}^{3} - {24y}^{2} + 6y { - 4y}^{2} + 4y - 1 \\ \\ resposta : {32y}^{5} - {84y}^{4} - {40y}^{2} + 10y - 1$




$c)(x + \frac{1}{x})^{6} \\ \\ (x + \frac{1}{x} )^{3 + 3} \\ (x + \frac{1}{3} )^{3} \times (x + \frac{1}{x} )^{3} \\ ( {x}^{3} + \frac{ {3x}^{2} }{x} + \frac{3x}{ {x}^{2} } + \frac{1}{ {x}^{3} } ) \times ( {x}^{3} + \frac{ {3x}^{2} }{x} + \frac{3x}{ {x}^{2} } + \frac{1}{ {x}^{3} } \\ {x}^{6} + {6x}^{4} + {15x}^{2} + 20 + \frac{6}{ {x}^{2} } + \frac{9}{ {x}^{2} } + \frac{6}{ {x}^{4} } + \frac{1}{ {x}^{6} } \\ \frac{ {x}^{12} + {6x}^{10} + {15x}^{8} + {20x}^{6} + {6x}^{4} + {9x}^{4} + {6x}^{2} + 1 }{ {x}^{2} } \\ \\ \\ resposta : \frac{ {x}^{12} + {6x}^{10} + {15x}^{8} + {20x}^{6} + {15x}^{4} + {6x}^{2} + 1}{ {x}^{6} }$




Espero ter ajudado. Bons estudos!!