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受欢迎的代数 >

展开 (x^2+3)^6

解答

展开

(x^{2} + 3)^{6}

解答

x^{12} + 18 x^{10} + 135 x^{8} + 540 x^{6} + 1215 x^{4} + 1458 x^{2} + 729

求解步骤

(x^{2} + 3)^{6}

使用二项式定理:

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

a = x^{2}, b = 3

= i = 0 \sum 6 (i 6) (x^{2})^{(6 - i)} \cdot 3^{i}

展开求和

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

化简

\frac{6 !}{0 ! ( 6 - 0 ) !} (x^{2})^{6} \cdot 3^{0} : x^{12}

化简

\frac{6 !}{1 ! ( 6 - 1 ) !} (x^{2})^{5} \cdot 3^{1} : 18 x^{10}

化简

\frac{6 !}{2 ! ( 6 - 2 ) !} (x^{2})^{4} \cdot 3^{2} : 135 x^{8}

化简

\frac{6 !}{3 ! ( 6 - 3 ) !} (x^{2})^{3} \cdot 3^{3} : 540 x^{6}

化简

\frac{6 !}{4 ! ( 6 - 4 ) !} (x^{2})^{2} \cdot 3^{4} : 1215 x^{4}

化简

\frac{6 !}{5 ! ( 6 - 5 ) !} (x^{2})^{1} \cdot 3^{5} : 1458 x^{2}

化简

\frac{6 !}{6 ! ( 6 - 6 ) !} (x^{2})^{0} \cdot 3^{6} : 729

= x^{12} + 18 x^{10} + 135 x^{8} + 540 x^{6} + 1215 x^{4} + 1458 x^{2} + 729

流行的例子

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s im pl i f y \frac{32}{3}

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f a c t or 8 x^{3} + z^{3}

s im pl i f y \frac{12}{18}

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s im pl i f y (1 + (1 + (1 + x^{3})^{4})^{5})^{6}

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s im pl i f y \frac{1}{81}