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Popular Álgebra >

expandir (sqrt(2)-j^2)^8

Solução

expandir

(2 - j^{2})^{8}

Solução

16 - 642 j^{2} + 224 j^{4} - 2242 j^{6} + 280 j^{8} - 1122 j^{10} + 56 j^{12} - 82 j^{14} + j^{16}

Passos da solução

(2 - j^{2})^{8}

Aplicar o teorema do binômio:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 2, b = - j^{2}

= i = 0 \sum 8 (i 8) (2)^{(8 - i)} (- j^{2})^{i}

Expandir a soma

= \frac{8 !}{0 ! ( 8 - 0 ) !} (2)^{8} (- j^{2})^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} (2)^{7} (- j^{2})^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} (2)^{6} (- j^{2})^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} (2)^{5} (- j^{2})^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} (2)^{4} (- j^{2})^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} (2)^{3} (- j^{2})^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} (2)^{2} (- j^{2})^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} (2)^{1} (- j^{2})^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} (2)^{0} (- j^{2})^{8}

Simplificar

\frac{8 !}{0 ! ( 8 - 0 ) !} (2)^{8} (- j^{2})^{0} : 16

Simplificar

\frac{8 !}{1 ! ( 8 - 1 ) !} (2)^{7} (- j^{2})^{1} : - 642 j^{2}

Simplificar

\frac{8 !}{2 ! ( 8 - 2 ) !} (2)^{6} (- j^{2})^{2} : 224 j^{4}

Simplificar

\frac{8 !}{3 ! ( 8 - 3 ) !} (2)^{5} (- j^{2})^{3} : - 2242 j^{6}

Simplificar

\frac{8 !}{4 ! ( 8 - 4 ) !} (2)^{4} (- j^{2})^{4} : 280 j^{8}

Simplificar

\frac{8 !}{5 ! ( 8 - 5 ) !} (2)^{3} (- j^{2})^{5} : - 1122 j^{10}

Simplificar

\frac{8 !}{6 ! ( 8 - 6 ) !} (2)^{2} (- j^{2})^{6} : 56 j^{12}

Simplificar

\frac{8 !}{7 ! ( 8 - 7 ) !} (2)^{1} (- j^{2})^{7} : - 82 j^{14}

Simplificar

\frac{8 !}{8 ! ( 8 - 8 ) !} (2)^{0} (- j^{2})^{8} : j^{16}

= 16 - 642 j^{2} + 224 j^{4} - 2242 j^{6} + 280 j^{8} - 1122 j^{10} + 56 j^{12} - 82 j^{14} + j^{16}

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