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人気のある代数 >

展開する (sqrt(x)+2x^2)^6

解

展開する

(x + 2 x^{2})^{6}

解

x^{3} + 12 x^{9} + 60 x^{6} + 160 x^{15} + 240 x^{9} + 192 x^{21} + 64 x^{12}

解答ステップ

(x + 2 x^{2})^{6}

2項定理を適用する:

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

a = x, b = 2 x^{2}

= i = 0 \sum 6 (i 6) (x)^{(6 - i)} (2 x^{2})^{i}

総和を展開する

= \frac{6 !}{0 ! ( 6 - 0 ) !} (x)^{6} (2 x^{2})^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (x)^{5} (2 x^{2})^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (x)^{4} (2 x^{2})^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (x)^{3} (2 x^{2})^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (x)^{2} (2 x^{2})^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (x)^{1} (2 x^{2})^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (x)^{0} (2 x^{2})^{6}

簡素化

\frac{6 !}{0 ! ( 6 - 0 ) !} (x)^{6} (2 x^{2})^{0} : x^{3}

簡素化

\frac{6 !}{1 ! ( 6 - 1 ) !} (x)^{5} (2 x^{2})^{1} : 12 x^{2} (x)^{5}

簡素化

\frac{6 !}{2 ! ( 6 - 2 ) !} (x)^{4} (2 x^{2})^{2} : 60 x^{6}

簡素化

\frac{6 !}{3 ! ( 6 - 3 ) !} (x)^{3} (2 x^{2})^{3} : 160 x^{6} (x)^{3}

簡素化

\frac{6 !}{4 ! ( 6 - 4 ) !} (x)^{2} (2 x^{2})^{4} : 240 x^{9}

簡素化

\frac{6 !}{5 ! ( 6 - 5 ) !} (x)^{1} (2 x^{2})^{5} : 192 x^{10} x

簡素化

\frac{6 !}{6 ! ( 6 - 6 ) !} (x)^{0} (2 x^{2})^{6} : 64 x^{12}

= x^{3} + 12 x^{2} (x)^{5} + 60 x^{6} + 160 x^{6} (x)^{3} + 240 x^{9} + 192 x^{10} x + 64 x^{12}

12 x^{2} (x)^{5} = 12 x^{\frac{9}{2}}

160 x^{6} (x)^{3} = 160 x^{\frac{15}{2}}

192 x^{10} x = 192 x^{\frac{21}{2}}

= x^{3} + 12 x^{\frac{9}{2}} + 60 x^{6} + 160 x^{\frac{15}{2}} + 240 x^{9} + 192 x^{\frac{21}{2}} + 64 x^{12}

簡素化

x^{3} + 12 x^{\frac{9}{2}} + 60 x^{6} + 160 x^{\frac{15}{2}} + 240 x^{9} + 192 x^{\frac{21}{2}} + 64 x^{12} : x^{3} + 12 x^{9} + 60 x^{6} + 160 x^{15} + 240 x^{9} + 192 x^{21} + 64 x^{12}

= x^{3} + 12 x^{9} + 60 x^{6} + 160 x^{15} + 240 x^{9} + 192 x^{21} + 64 x^{12}

人気の例

s im pl i f y \frac{4}{a} - \frac{3}{b}

簡約 14-3x^2-5sqrt(7x)

s im pl i f y 14 - 3 x^{2} - 5 7 x

因数 32u^2v-50v

f a c t or 32 u^{2} v - 50 v

簡約 (-a*b^5*c^1*1)^6

s im pl i f y (- a \cdot b^{5} \cdot c^{1} \cdot 1)^{6}

展開する 2(3x+3)^2

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