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受欢迎的代数 >

展开 (3x+2y^2)^5

解答

展开

(3 x + 2 y^{2})^{5}

解答

243 x^{5} + 810 x^{4} y^{2} + 1080 x^{3} y^{4} + 720 x^{2} y^{6} + 240 x y^{8} + 32 y^{10}

求解步骤

(3 x + 2 y^{2})^{5}

使用二项式定理:

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

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

= i = 0 \sum 5 (i 5) (3 x)^{(5 - i)} (2 y^{2})^{i}

展开求和

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

化简

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} (2 y^{2})^{0} : 243 x^{5}

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} (2 y^{2})^{1} : 810 x^{4} y^{2}

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} (2 y^{2})^{2} : 1080 x^{3} y^{4}

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} (2 y^{2})^{3} : 720 x^{2} y^{6}

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} (2 y^{2})^{4} : 240 x y^{8}

化简

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} (2 y^{2})^{5} : 32 y^{10}

= 243 x^{5} + 810 x^{4} y^{2} + 1080 x^{3} y^{4} + 720 x^{2} y^{6} + 240 x y^{8} + 32 y^{10}

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