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受欢迎的代数 >

展开 (\sqrt[5]{12}x+y)^5

解答

展开

(512 x + y)^{5}

解答

12 x^{5} + 5 5 1 2^{4} x^{4} y + 10 5 1 2^{3} x^{3} y^{2} + 10 5 1 2^{2} x^{2} y^{3} + 5512 x y^{4} + y^{5}

求解步骤

(512 x + y)^{5}

使用二项式定理:

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

a = 512 x, b = y

= i = 0 \sum 5 (i 5) (512 x)^{(5 - i)} y^{i}

展开求和

= \frac{5 !}{0 ! ( 5 - 0 ) !} (512 x)^{5} y^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (512 x)^{4} y^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (512 x)^{3} y^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (512 x)^{2} y^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (512 x)^{1} y^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (512 x)^{0} y^{5}

化简

\frac{5 !}{0 ! ( 5 - 0 ) !} (512 x)^{5} y^{0} : 12 x^{5}

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} (512 x)^{4} y^{1} : 5 \cdot 1 2^{\frac{4}{5}} x^{4} y

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} (512 x)^{3} y^{2} : 10 \cdot 1 2^{\frac{3}{5}} x^{3} y^{2}

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} (512 x)^{2} y^{3} : 10 \cdot 1 2^{\frac{2}{5}} x^{2} y^{3}

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} (512 x)^{1} y^{4} : 5512 x y^{4}

化简

\frac{5 !}{5 ! ( 5 - 5 ) !} (512 x)^{0} y^{5} : y^{5}

= 12 x^{5} + 5 \cdot 1 2^{\frac{4}{5}} x^{4} y + 10 \cdot 1 2^{\frac{3}{5}} x^{3} y^{2} + 10 \cdot 1 2^{\frac{2}{5}} x^{2} y^{3} + 5512 x y^{4} + y^{5}

化简

12 x^{5} + 5 \cdot 1 2^{\frac{4}{5}} x^{4} y + 10 \cdot 1 2^{\frac{3}{5}} x^{3} y^{2} + 10 \cdot 1 2^{\frac{2}{5}} x^{2} y^{3} + 5512 x y^{4} + y^{5} : 12 x^{5} + 5 5 1 2^{4} x^{4} y + 10 5 1 2^{3} x^{3} y^{2} + 10 5 1 2^{2} x^{2} y^{3} + 5512 x y^{4} + y^{5}

= 12 x^{5} + 5 5 1 2^{4} x^{4} y + 10 5 1 2^{3} x^{3} y^{2} + 10 5 1 2^{2} x^{2} y^{3} + 5512 x y^{4} + y^{5}

流行的例子

展开 1/((x)(x^2+2s+36))

e x p an d \frac{1}{( x ) ( x ^{2} + 2 s + 36 )}

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s im pl i f y 1 + \frac{k}{s ^{2} + ( 5 + k ) s + 0.5}

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e x p an d \frac{3 ( 3 x - 2 )}{x - 4}

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s im pl i f y (2 - 2) (2 + 2)

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e x p an d \frac{3 x + 2}{( x - 3 ) ( x + 2 )}