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受欢迎的代数 >

展开 (3x^2-sqrt(y))^9

解答

展开

(3 x^{2} - y)^{9}

解答

19683 x^{18} - 59049 x^{16} y + 78732 x^{14} y - 61236 x^{12} y y + 30618 x^{10} y^{2} - 10206 x^{8} y^{2} y + 2268 x^{6} y^{3} - 324 x^{4} y^{3} y + 27 x^{2} y^{4} - y^{4} y

求解步骤

(3 x^{2} - y)^{9}

使用二项式定理:

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

a = 3 x^{2}, b = - y

= i = 0 \sum 9 (i 9) (3 x^{2})^{(9 - i)} (- y)^{i}

展开求和

= \frac{9 !}{0 ! ( 9 - 0 ) !} (3 x^{2})^{9} (- y)^{0} + \frac{9 !}{1 ! ( 9 - 1 ) !} (3 x^{2})^{8} (- y)^{1} + \frac{9 !}{2 ! ( 9 - 2 ) !} (3 x^{2})^{7} (- y)^{2} + \frac{9 !}{3 ! ( 9 - 3 ) !} (3 x^{2})^{6} (- y)^{3} + \frac{9 !}{4 ! ( 9 - 4 ) !} (3 x^{2})^{5} (- y)^{4} + \frac{9 !}{5 ! ( 9 - 5 ) !} (3 x^{2})^{4} (- y)^{5} + \frac{9 !}{6 ! ( 9 - 6 ) !} (3 x^{2})^{3} (- y)^{6} + \frac{9 !}{7 ! ( 9 - 7 ) !} (3 x^{2})^{2} (- y)^{7} + \frac{9 !}{8 ! ( 9 - 8 ) !} (3 x^{2})^{1} (- y)^{8} + \frac{9 !}{9 ! ( 9 - 9 ) !} (3 x^{2})^{0} (- y)^{9}

化简

\frac{9 !}{0 ! ( 9 - 0 ) !} (3 x^{2})^{9} (- y)^{0} : 19683 x^{18}

化简

\frac{9 !}{1 ! ( 9 - 1 ) !} (3 x^{2})^{8} (- y)^{1} : - 59049 x^{16} y

化简

\frac{9 !}{2 ! ( 9 - 2 ) !} (3 x^{2})^{7} (- y)^{2} : 78732 x^{14} y

化简

\frac{9 !}{3 ! ( 9 - 3 ) !} (3 x^{2})^{6} (- y)^{3} : - 61236 x^{12} (y)^{3}

化简

\frac{9 !}{4 ! ( 9 - 4 ) !} (3 x^{2})^{5} (- y)^{4} : 30618 x^{10} y^{2}

化简

\frac{9 !}{5 ! ( 9 - 5 ) !} (3 x^{2})^{4} (- y)^{5} : - 10206 x^{8} (y)^{5}

化简

\frac{9 !}{6 ! ( 9 - 6 ) !} (3 x^{2})^{3} (- y)^{6} : 2268 x^{6} y^{3}

化简

\frac{9 !}{7 ! ( 9 - 7 ) !} (3 x^{2})^{2} (- y)^{7} : - 324 x^{4} (y)^{7}

化简

\frac{9 !}{8 ! ( 9 - 8 ) !} (3 x^{2})^{1} (- y)^{8} : 27 x^{2} y^{4}

化简

\frac{9 !}{9 ! ( 9 - 9 ) !} (3 x^{2})^{0} (- y)^{9} : - (y)^{9}

= 19683 x^{18} - 59049 x^{16} y + 78732 x^{14} y - 61236 x^{12} (y)^{3} + 30618 x^{10} y^{2} - 10206 x^{8} (y)^{5} + 2268 x^{6} y^{3} - 324 x^{4} (y)^{7} + 27 x^{2} y^{4} - (y)^{9}

(y)^{3} = y y

(y)^{5} = y^{2} y

(y)^{7} = y^{3} y

(y)^{9} = y^{4} y

= 19683 x^{18} - 59049 x^{16} y + 78732 x^{14} y - 61236 x^{12} y y + 30618 x^{10} y^{2} - 10206 x^{8} y^{2} y + 2268 x^{6} y^{3} - 324 x^{4} y^{3} y + 27 x^{2} y^{4} - y^{4} y

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