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受欢迎的代数 >

展开 (x^2+pi)^4

解答

展开

(x^{2} + π)^{4}

解答

x^{8} + 4 π x^{6} + 6 π^{2} x^{4} + 4 π^{3} x^{2} + π^{4}

求解步骤

(x^{2} + π)^{4}

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 = π

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} π^{i}

展开求和

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

化简

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} π^{0} : x^{8}

化简

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} π^{1} : 4 π x^{6}

化简

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} π^{2} : 6 π^{2} x^{4}

化简

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} π^{3} : 4 π^{3} x^{2}

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} π^{4} = π^{4}

= x^{8} + 4 π x^{6} + 6 π^{2} x^{4} + 4 π^{3} x^{2} + π^{4}

流行的例子

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