ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع الجبر >

expand (1/(x^3)-x^2)^{18}

الحلّ

expand

(\frac{1}{x ^{3}} - x^{2})^{18}

الحلّ

\frac{1}{x ^{54}} - \frac{18}{x ^{49}} + \frac{153}{x ^{44}} - \frac{816}{x ^{39}} + \frac{3060}{x ^{34}} - \frac{8568}{x ^{29}} + \frac{18564}{x ^{24}} - \frac{31824}{x ^{19}} + \frac{43758}{x ^{14}} - \frac{48620}{x ^{9}} + \frac{43758}{x ^{4}} - 31824 x + 18564 x^{6} - 8568 x^{11} + 3060 x^{16} - 816 x^{21} + 153 x^{26} - 18 x^{31} + x^{36}

خطوات الحلّ

(\frac{1}{x ^{3}} - x^{2})^{18}

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

:فعّل نظريّة ذات الحدّين لنيوتن

a = \frac{1}{x ^{3}}, b = - x^{2}

= i = 0 \sum 18 (i 18) (\frac{1}{x ^{3}})^{(18 - i)} (- x^{2})^{i}

وسّع حاصل الجمع

= \frac{18 !}{0 ! ( 18 - 0 ) !} (\frac{1}{x ^{3}})^{18} (- x^{2})^{0} + \frac{18 !}{1 ! ( 18 - 1 ) !} (\frac{1}{x ^{3}})^{17} (- x^{2})^{1} + \frac{18 !}{2 ! ( 18 - 2 ) !} (\frac{1}{x ^{3}})^{16} (- x^{2})^{2} + \frac{18 !}{3 ! ( 18 - 3 ) !} (\frac{1}{x ^{3}})^{15} (- x^{2})^{3} + \frac{18 !}{4 ! ( 18 - 4 ) !} (\frac{1}{x ^{3}})^{14} (- x^{2})^{4} + \frac{18 !}{5 ! ( 18 - 5 ) !} (\frac{1}{x ^{3}})^{13} (- x^{2})^{5} + \frac{18 !}{6 ! ( 18 - 6 ) !} (\frac{1}{x ^{3}})^{12} (- x^{2})^{6} + \frac{18 !}{7 ! ( 18 - 7 ) !} (\frac{1}{x ^{3}})^{11} (- x^{2})^{7} + \frac{18 !}{8 ! ( 18 - 8 ) !} (\frac{1}{x ^{3}})^{10} (- x^{2})^{8} + \frac{18 !}{9 ! ( 18 - 9 ) !} (\frac{1}{x ^{3}})^{9} (- x^{2})^{9} + \frac{18 !}{10 ! ( 18 - 10 ) !} (\frac{1}{x ^{3}})^{8} (- x^{2})^{10} + \frac{18 !}{11 ! ( 18 - 11 ) !} (\frac{1}{x ^{3}})^{7} (- x^{2})^{11} + \frac{18 !}{12 ! ( 18 - 12 ) !} (\frac{1}{x ^{3}})^{6} (- x^{2})^{12} + \frac{18 !}{13 ! ( 18 - 13 ) !} (\frac{1}{x ^{3}})^{5} (- x^{2})^{13} + \frac{18 !}{14 ! ( 18 - 14 ) !} (\frac{1}{x ^{3}})^{4} (- x^{2})^{14} + \frac{18 !}{15 ! ( 18 - 15 ) !} (\frac{1}{x ^{3}})^{3} (- x^{2})^{15} + \frac{18 !}{16 ! ( 18 - 16 ) !} (\frac{1}{x ^{3}})^{2} (- x^{2})^{16} + \frac{18 !}{17 ! ( 18 - 17 ) !} (\frac{1}{x ^{3}})^{1} (- x^{2})^{17} + \frac{18 !}{18 ! ( 18 - 18 ) !} (\frac{1}{x ^{3}})^{0} (- x^{2})^{18}

\frac{18 !}{0 ! ( 18 - 0 ) !} (\frac{1}{x ^{3}})^{18} (- x^{2})^{0}

بسّط:

\frac{1}{x ^{54}}

\frac{18 !}{1 ! ( 18 - 1 ) !} (\frac{1}{x ^{3}})^{17} (- x^{2})^{1}

بسّط:

- \frac{18}{x ^{49}}

\frac{18 !}{2 ! ( 18 - 2 ) !} (\frac{1}{x ^{3}})^{16} (- x^{2})^{2}

بسّط:

\frac{153}{x ^{44}}

\frac{18 !}{3 ! ( 18 - 3 ) !} (\frac{1}{x ^{3}})^{15} (- x^{2})^{3}

بسّط:

- \frac{816}{x ^{39}}

\frac{18 !}{4 ! ( 18 - 4 ) !} (\frac{1}{x ^{3}})^{14} (- x^{2})^{4}

بسّط:

\frac{3060}{x ^{34}}

\frac{18 !}{5 ! ( 18 - 5 ) !} (\frac{1}{x ^{3}})^{13} (- x^{2})^{5}

بسّط:

- \frac{8568}{x ^{29}}

\frac{18 !}{6 ! ( 18 - 6 ) !} (\frac{1}{x ^{3}})^{12} (- x^{2})^{6}

بسّط:

\frac{18564}{x ^{24}}

\frac{18 !}{7 ! ( 18 - 7 ) !} (\frac{1}{x ^{3}})^{11} (- x^{2})^{7}

بسّط:

- \frac{31824}{x ^{19}}

\frac{18 !}{8 ! ( 18 - 8 ) !} (\frac{1}{x ^{3}})^{10} (- x^{2})^{8}

بسّط:

\frac{43758}{x ^{14}}

\frac{18 !}{9 ! ( 18 - 9 ) !} (\frac{1}{x ^{3}})^{9} (- x^{2})^{9}

بسّط:

- \frac{48620}{x ^{9}}

\frac{18 !}{10 ! ( 18 - 10 ) !} (\frac{1}{x ^{3}})^{8} (- x^{2})^{10}

بسّط:

\frac{43758}{x ^{4}}

\frac{18 !}{11 ! ( 18 - 11 ) !} (\frac{1}{x ^{3}})^{7} (- x^{2})^{11}

بسّط:

- 31824 x

\frac{18 !}{12 ! ( 18 - 12 ) !} (\frac{1}{x ^{3}})^{6} (- x^{2})^{12}

بسّط:

18564 x^{6}

\frac{18 !}{13 ! ( 18 - 13 ) !} (\frac{1}{x ^{3}})^{5} (- x^{2})^{13}

بسّط:

- 8568 x^{11}

\frac{18 !}{14 ! ( 18 - 14 ) !} (\frac{1}{x ^{3}})^{4} (- x^{2})^{14}

بسّط:

3060 x^{16}

\frac{18 !}{15 ! ( 18 - 15 ) !} (\frac{1}{x ^{3}})^{3} (- x^{2})^{15}

بسّط:

- 816 x^{21}

\frac{18 !}{16 ! ( 18 - 16 ) !} (\frac{1}{x ^{3}})^{2} (- x^{2})^{16}

بسّط:

153 x^{26}

\frac{18 !}{17 ! ( 18 - 17 ) !} (\frac{1}{x ^{3}})^{1} (- x^{2})^{17}

بسّط:

- 18 x^{31}

\frac{18 !}{18 ! ( 18 - 18 ) !} (\frac{1}{x ^{3}})^{0} (- x^{2})^{18}

بسّط:

x^{36}

= \frac{1}{x ^{54}} - \frac{18}{x ^{49}} + \frac{153}{x ^{44}} - \frac{816}{x ^{39}} + \frac{3060}{x ^{34}} - \frac{8568}{x ^{29}} + \frac{18564}{x ^{24}} - \frac{31824}{x ^{19}} + \frac{43758}{x ^{14}} - \frac{48620}{x ^{9}} + \frac{43758}{x ^{4}} - 31824 x + 18564 x^{6} - 8568 x^{11} + 3060 x^{16} - 816 x^{21} + 153 x^{26} - 18 x^{31} + x^{36}

أمثلة شائعة

expand 18.75*(1-e^{-0.91*(t+0.01)})

e x p an d 18.75 \cdot (1 - e^{- 0.91 \cdot (t + 0.01)})

expand (s/2-1)^6

e x p an d (\frac{s}{2} - 1)^{6}

expand 1/4 (1-sin(4x))-2cos^2(x)sin^2(x)

e x p an d \frac{1}{4} (1 - sin (4 x)) - 2 cos^{2} (x) sin^{2} (x)

simplify 10(sec^2(x)+csc^2(x))

s im pl i f y 10 (sec^{2} (x) + csc^{2} (x))

expand cos(x)(-sin(x)+1)

e x p an d cos (x) (- sin (x) + 1)