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受欢迎的代数 >

展开 (x^2+y^2)^5

解答

展开

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

解答

x^{10} + 5 x^{8} y^{2} + 10 x^{6} y^{4} + 10 x^{4} y^{6} + 5 x^{2} y^{8} + y^{10}

求解步骤

(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 = x^{2}, b = y^{2}

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

展开求和

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

化简

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

化简

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

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} (y^{2})^{2} : 10 x^{6} y^{4}

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} (y^{2})^{3} : 10 x^{4} y^{6}

化简

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

化简

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

= x^{10} + 5 x^{8} y^{2} + 10 x^{6} y^{4} + 10 x^{4} y^{6} + 5 x^{2} y^{8} + y^{10}

流行的例子

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s im pl i f y 3 \cdot 1028

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s im pl i f y x^{2} \cdot x^{- 4}

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s im pl i f y - \frac{11}{10} + (- \frac{7}{4})

展开 (x-2)(x+2)(x^2+4)(x^4+16)

e x p an d (x - 2) (x + 2) (x^{2} + 4) (x^{4} + 16)