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受欢迎的代数 >

展开 (x^2+3)^5

解答

展开

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

解答

x^{10} + 15 x^{8} + 90 x^{6} + 270 x^{4} + 405 x^{2} + 243

求解步骤

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

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 5 (i 5) (x^{2})^{(5 - i)} \cdot 3^{i}

展开求和

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

化简

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

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} (x^{2})^{4} \cdot 3^{1} : 15 x^{8}

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} \cdot 3^{2} : 90 x^{6}

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} \cdot 3^{3} : 270 x^{4}

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} (x^{2})^{1} \cdot 3^{4} : 405 x^{2}

化简

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

= x^{10} + 15 x^{8} + 90 x^{6} + 270 x^{4} + 405 x^{2} + 243

流行的例子

展开 (-4x+5)^2

e x p an d (- 4 x + 5)^{2}

因式分解 6x^5y+2xy^3-6y

f a c t or 6 x^{5} y + 2 x y^{3} - 6 y

展开 (2x^3+y^2)^2

e x p an d (2 x^{3} + y^{2})^{2}

化简 (6x)^{-2}

s im pl i f y (6 x)^{- 2}

s im pl i f y \frac{5}{6} - \frac{2}{6}