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Popular Álgebra >

expandir (3+2b)^8

Solução

expandir

(3 + 2 b)^{8}

Solução

6561 + 34992 b + 81648 b^{2} + 108864 b^{3} + 90720 b^{4} + 48384 b^{5} + 16128 b^{6} + 3072 b^{7} + 256 b^{8}

Passos da solução

(3 + 2 b)^{8}

Aplicar o teorema do binômio:

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

a = 3, b = 2 b

= i = 0 \sum 8 (i 8) \cdot 3^{(8 - i)} (2 b)^{i}

Expandir a soma

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

Simplificar

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 3^{8} (2 b)^{0} : 6561

Simplificar

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 3^{7} (2 b)^{1} : 34992 b

Simplificar

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 3^{6} (2 b)^{2} : 81648 b^{2}

Simplificar

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 3^{5} (2 b)^{3} : 108864 b^{3}

Simplificar

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 3^{4} (2 b)^{4} : 90720 b^{4}

Simplificar

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 3^{3} (2 b)^{5} : 48384 b^{5}

Simplificar

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 3^{2} (2 b)^{6} : 16128 b^{6}

Simplificar

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 3^{1} (2 b)^{7} : 3072 b^{7}

Simplificar

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 3^{0} (2 b)^{8} : 256 b^{8}

= 6561 + 34992 b + 81648 b^{2} + 108864 b^{3} + 90720 b^{4} + 48384 b^{5} + 16128 b^{6} + 3072 b^{7} + 256 b^{8}

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