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Popular Álgebra >

expandir (2a-3b)^6

Solução

expandir

(2 a - 3 b)^{6}

Solução

64 a^{6} - 576 a^{5} b + 2160 a^{4} b^{2} - 4320 a^{3} b^{3} + 4860 a^{2} b^{4} - 2916 a b^{5} + 729 b^{6}

Passos da solução

(2 a - 3 b)^{6}

Aplicar o teorema do binômio:

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

a = 2 a, b = - 3 b

= i = 0 \sum 6 (i 6) (2 a)^{(6 - i)} (- 3 b)^{i}

Expandir a soma

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

Simplificar

\frac{6 !}{0 ! ( 6 - 0 ) !} (2 a)^{6} (- 3 b)^{0} : 64 a^{6}

Simplificar

\frac{6 !}{1 ! ( 6 - 1 ) !} (2 a)^{5} (- 3 b)^{1} : - 576 a^{5} b

Simplificar

\frac{6 !}{2 ! ( 6 - 2 ) !} (2 a)^{4} (- 3 b)^{2} : 2160 a^{4} b^{2}

Simplificar

\frac{6 !}{3 ! ( 6 - 3 ) !} (2 a)^{3} (- 3 b)^{3} : - 4320 a^{3} b^{3}

Simplificar

\frac{6 !}{4 ! ( 6 - 4 ) !} (2 a)^{2} (- 3 b)^{4} : 4860 a^{2} b^{4}

Simplificar

\frac{6 !}{5 ! ( 6 - 5 ) !} (2 a)^{1} (- 3 b)^{5} : - 2916 a b^{5}

Simplificar

\frac{6 !}{6 ! ( 6 - 6 ) !} (2 a)^{0} (- 3 b)^{6} : 729 b^{6}

= 64 a^{6} - 576 a^{5} b + 2160 a^{4} b^{2} - 4320 a^{3} b^{3} + 4860 a^{2} b^{4} - 2916 a b^{5} + 729 b^{6}

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