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受欢迎的代数 >

展开 (2ysin(x)+x^2)^5

解答

展开

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

解答

32 y^{5} sin^{5} (x) + 80 y^{4} x^{2} sin^{4} (x) + 80 y^{3} x^{4} sin^{3} (x) + 40 y^{2} x^{6} sin^{2} (x) + 10 y x^{8} sin (x) + x^{10}

求解步骤

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

使用二项式定理:

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

a = 2 y sin (x), b = x^{2}

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

展开求和

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

化简

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

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 y sin (x))^{4} (x^{2})^{1} : 80 y^{4} x^{2} sin^{4} (x)

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 y sin (x))^{3} (x^{2})^{2} : 80 y^{3} x^{4} sin^{3} (x)

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 y sin (x))^{2} (x^{2})^{3} : 40 y^{2} x^{6} sin^{2} (x)

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 y sin (x))^{1} (x^{2})^{4} : 10 y x^{8} sin (x)

化简

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

= 32 y^{5} sin^{5} (x) + 80 y^{4} x^{2} sin^{4} (x) + 80 y^{3} x^{4} sin^{3} (x) + 40 y^{2} x^{6} sin^{2} (x) + 10 y x^{8} sin (x) + x^{10}

流行的例子

展开-1+2(x-(3pi)/4)

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e x p an d (r cos (θ) - r sin (θ))^{2}

展开-(5(5+sqrt(41)))/4

e x p an d - \frac{5 ( 5 + 41 )}{4}

化简 (4-sqrt(14-x))(4+sqrt(14-x))

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