he

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

פּוֹפּוּלָרִי אלגברה >

expand (7-\sqrt[3]{x/(13841287201)})^{17}

פתרון

expand

(7 - 3 \frac{x}{13841287201})^{17}

פתרון

7^{17} - \frac{7 ^{16} \cdot 17 3 x}{3 13841287201} + 7^{15} \cdot 136 (3 \frac{x}{13841287201})^{2} - 33320 x + 16660 x 3 \frac{x}{13841287201} - \frac{6188 x 3 x ^{2}}{3 1384128720 1 ^{2}} + \frac{7 ^{11} \cdot 12376 x ^{2}}{1384128720 1 ^{2}} - \frac{19448 3 x ^{7}}{282475249 3 1384128720 1 ^{2}} + \frac{980996186170 x ^{2} 3 x ^{2}}{1384128720 1 ^{2} 3 1384128720 1 ^{2}} - \frac{140142312310 x ^{3}}{1384128720 1 ^{3}} + \frac{6670664 3 x ^{10}}{1384128720 1 ^{3}} - \frac{1456024024 x ^{3} 3 x ^{2}}{1384128720 1 ^{3} 3 1384128720 1 ^{2}} + \frac{104001716 x ^{4}}{1384128720 1 ^{4}} - \frac{2380 3 x ^{13}}{1384128720 1 ^{4}} + \frac{233240 x ^{4} 3 x ^{2}}{1384128720 1 ^{4} 3 1384128720 1 ^{2}} - \frac{6664 x ^{5}}{1384128720 1 ^{5}} + \frac{17 3 x ^{16}}{1384128720 1 ^{5} \cdot 343} - \frac{x ^{5} ( 3 \frac{x}{13841287201} ) ^{2}}{1384128720 1 ^{5}}

צעדי פתרון

(7 - 3 \frac{x}{13841287201})^{17}

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

:הפעל את הבינום של ניוטון

a = 7, b = - 3 \frac{x}{13841287201}

= i = 0 \sum 17 (i 17) \cdot 7^{(17 - i)} (- 3 \frac{x}{13841287201})^{i}

הרחב את הסכום

= \frac{17 !}{0 ! ( 17 - 0 ) !} \cdot 7^{17} (- 3 \frac{x}{13841287201})^{0} + \frac{17 !}{1 ! ( 17 - 1 ) !} \cdot 7^{16} (- 3 \frac{x}{13841287201})^{1} + \frac{17 !}{2 ! ( 17 - 2 ) !} \cdot 7^{15} (- 3 \frac{x}{13841287201})^{2} + \frac{17 !}{3 ! ( 17 - 3 ) !} \cdot 7^{14} (- 3 \frac{x}{13841287201})^{3} + \frac{17 !}{4 ! ( 17 - 4 ) !} \cdot 7^{13} (- 3 \frac{x}{13841287201})^{4} + \frac{17 !}{5 ! ( 17 - 5 ) !} \cdot 7^{12} (- 3 \frac{x}{13841287201})^{5} + \frac{17 !}{6 ! ( 17 - 6 ) !} \cdot 7^{11} (- 3 \frac{x}{13841287201})^{6} + \frac{17 !}{7 ! ( 17 - 7 ) !} \cdot 7^{10} (- 3 \frac{x}{13841287201})^{7} + \frac{17 !}{8 ! ( 17 - 8 ) !} \cdot 7^{9} (- 3 \frac{x}{13841287201})^{8} + \frac{17 !}{9 ! ( 17 - 9 ) !} \cdot 7^{8} (- 3 \frac{x}{13841287201})^{9} + \frac{17 !}{10 ! ( 17 - 10 ) !} \cdot 7^{7} (- 3 \frac{x}{13841287201})^{10} + \frac{17 !}{11 ! ( 17 - 11 ) !} \cdot 7^{6} (- 3 \frac{x}{13841287201})^{11} + \frac{17 !}{12 ! ( 17 - 12 ) !} \cdot 7^{5} (- 3 \frac{x}{13841287201})^{12} + \frac{17 !}{13 ! ( 17 - 13 ) !} \cdot 7^{4} (- 3 \frac{x}{13841287201})^{13} + \frac{17 !}{14 ! ( 17 - 14 ) !} \cdot 7^{3} (- 3 \frac{x}{13841287201})^{14} + \frac{17 !}{15 ! ( 17 - 15 ) !} \cdot 7^{2} (- 3 \frac{x}{13841287201})^{15} + \frac{17 !}{16 ! ( 17 - 16 ) !} \cdot 7^{1} (- 3 \frac{x}{13841287201})^{16} + \frac{17 !}{17 ! ( 17 - 17 ) !} \cdot 7^{0} (- 3 \frac{x}{13841287201})^{17}

\frac{17 !}{0 ! ( 17 - 0 ) !} \cdot 7^{17} (- 3 \frac{x}{13841287201})^{0}

פשט את:

7^{17}

\frac{17 !}{1 ! ( 17 - 1 ) !} \cdot 7^{16} (- 3 \frac{x}{13841287201})^{1}

פשט את:

- \frac{7 ^{16} \cdot 17 3 x}{3 13841287201}

\frac{17 !}{2 ! ( 17 - 2 ) !} \cdot 7^{15} (- 3 \frac{x}{13841287201})^{2}

פשט את:

7^{15} \cdot 136 (3 \frac{x}{13841287201})^{2}

\frac{17 !}{3 ! ( 17 - 3 ) !} \cdot 7^{14} (- 3 \frac{x}{13841287201})^{3}

פשט את:

- \frac{7 ^{14} \cdot 680 x}{13841287201}

\frac{17 !}{4 ! ( 17 - 4 ) !} \cdot 7^{13} (- 3 \frac{x}{13841287201})^{4}

פשט את:

7^{13} \cdot 2380 (3 \frac{x}{13841287201})^{4}

\frac{17 !}{5 ! ( 17 - 5 ) !} \cdot 7^{12} (- 3 \frac{x}{13841287201})^{5}

פשט את:

- 7^{12} \cdot 6188 (3 \frac{x}{13841287201})^{5}

\frac{17 !}{6 ! ( 17 - 6 ) !} \cdot 7^{11} (- 3 \frac{x}{13841287201})^{6}

פשט את:

\frac{7 ^{11} \cdot 12376 x ^{2}}{1384128720 1 ^{2}}

\frac{17 !}{7 ! ( 17 - 7 ) !} \cdot 7^{10} (- 3 \frac{x}{13841287201})^{7}

פשט את:

- 5493578642552 (3 \frac{x}{13841287201})^{7}

\frac{17 !}{8 ! ( 17 - 8 ) !} \cdot 7^{9} (- 3 \frac{x}{13841287201})^{8}

פשט את:

980996186170 (3 \frac{x}{13841287201})^{8}

\frac{17 !}{9 ! ( 17 - 9 ) !} \cdot 7^{8} (- 3 \frac{x}{13841287201})^{9}

פשט את:

- \frac{140142312310 x ^{3}}{1384128720 1 ^{3}}

\frac{17 !}{10 ! ( 17 - 10 ) !} \cdot 7^{7} (- 3 \frac{x}{13841287201})^{10}

פשט את:

16016264264 (3 \frac{x}{13841287201})^{10}

\frac{17 !}{11 ! ( 17 - 11 ) !} \cdot 7^{6} (- 3 \frac{x}{13841287201})^{11}

פשט את:

- 1456024024 (3 \frac{x}{13841287201})^{11}

\frac{17 !}{12 ! ( 17 - 12 ) !} \cdot 7^{5} (- 3 \frac{x}{13841287201})^{12}

פשט את:

\frac{104001716 x ^{4}}{1384128720 1 ^{4}}

\frac{17 !}{13 ! ( 17 - 13 ) !} \cdot 7^{4} (- 3 \frac{x}{13841287201})^{13}

פשט את:

- 5714380 (3 \frac{x}{13841287201})^{13}

\frac{17 !}{14 ! ( 17 - 14 ) !} \cdot 7^{3} (- 3 \frac{x}{13841287201})^{14}

פשט את:

233240 (3 \frac{x}{13841287201})^{14}

\frac{17 !}{15 ! ( 17 - 15 ) !} \cdot 7^{2} (- 3 \frac{x}{13841287201})^{15}

פשט את:

- \frac{6664 x ^{5}}{1384128720 1 ^{5}}

\frac{17 !}{16 ! ( 17 - 16 ) !} \cdot 7^{1} (- 3 \frac{x}{13841287201})^{16}

פשט את:

119 (3 \frac{x}{13841287201})^{16}

\frac{17 !}{17 ! ( 17 - 17 ) !} \cdot 7^{0} (- 3 \frac{x}{13841287201})^{17}

פשט את:

- (3 \frac{x}{13841287201})^{17}

= 7^{17} - \frac{7 ^{16} \cdot 17 3 x}{3 13841287201} + 7^{15} \cdot 136 (3 \frac{x}{13841287201})^{2} - \frac{7 ^{14} \cdot 680 x}{13841287201} + 7^{13} \cdot 2380 (3 \frac{x}{13841287201})^{4} - 7^{12} \cdot 6188 (3 \frac{x}{13841287201})^{5} + \frac{7 ^{11} \cdot 12376 x ^{2}}{1384128720 1 ^{2}} - 5493578642552 (3 \frac{x}{13841287201})^{7} + 980996186170 (3 \frac{x}{13841287201})^{8} - \frac{140142312310 x ^{3}}{1384128720 1 ^{3}} + 16016264264 (3 \frac{x}{13841287201})^{10} - 1456024024 (3 \frac{x}{13841287201})^{11} + \frac{104001716 x ^{4}}{1384128720 1 ^{4}} - 5714380 (3 \frac{x}{13841287201})^{13} + 233240 (3 \frac{x}{13841287201})^{14} - \frac{6664 x ^{5}}{1384128720 1 ^{5}} + 119 (3 \frac{x}{13841287201})^{16} - (3 \frac{x}{13841287201})^{17}

7^{17} - \frac{7 ^{16} \cdot 17 3 x}{3 13841287201} + 7^{15} \cdot 136 (3 \frac{x}{13841287201})^{2} - \frac{7 ^{14} \cdot 680 x}{13841287201} + 7^{13} \cdot 2380 (3 \frac{x}{13841287201})^{4} - 7^{12} \cdot 6188 (3 \frac{x}{13841287201})^{5} + \frac{7 ^{11} \cdot 12376 x ^{2}}{1384128720 1 ^{2}} - 5493578642552 (3 \frac{x}{13841287201})^{7} + 980996186170 (3 \frac{x}{13841287201})^{8} - \frac{140142312310 x ^{3}}{1384128720 1 ^{3}} + 16016264264 (3 \frac{x}{13841287201})^{10} - 1456024024 (3 \frac{x}{13841287201})^{11} + \frac{104001716 x ^{4}}{1384128720 1 ^{4}} - 5714380 (3 \frac{x}{13841287201})^{13} + 233240 (3 \frac{x}{13841287201})^{14} - \frac{6664 x ^{5}}{1384128720 1 ^{5}} + 119 (3 \frac{x}{13841287201})^{16} - (3 \frac{x}{13841287201})^{17}

פשט את:

7^{17} - \frac{7 ^{16} \cdot 17 3 x}{3 13841287201} + 7^{15} \cdot 136 (3 \frac{x}{13841287201})^{2} - 33320 x + 16660 x 3 \frac{x}{13841287201} - \frac{6188 x 3 x ^{2}}{3 1384128720 1 ^{2}} + \frac{7 ^{11} \cdot 12376 x ^{2}}{1384128720 1 ^{2}} - \frac{19448 x ^{\frac{7}{3}}}{282475249 \cdot 1384128720 1 ^{\frac{2}{3}}} + \frac{980996186170 x ^{2} 3 x ^{2}}{1384128720 1 ^{2} 3 1384128720 1 ^{2}} - \frac{140142312310 x ^{3}}{1384128720 1 ^{3}} + \frac{6670664 x ^{\frac{10}{3}}}{1384128720 1 ^{3}} - \frac{1456024024 x ^{3} 3 x ^{2}}{1384128720 1 ^{3} 3 1384128720 1 ^{2}} + \frac{104001716 x ^{4}}{1384128720 1 ^{4}} - \frac{2380 x ^{\frac{13}{3}}}{1384128720 1 ^{4}} + \frac{233240 x ^{4} 3 x ^{2}}{1384128720 1 ^{4} 3 1384128720 1 ^{2}} - \frac{6664 x ^{5}}{1384128720 1 ^{5}} + \frac{17 x ^{\frac{16}{3}}}{1384128720 1 ^{5} \cdot 343} - \frac{x ^{5} ( 3 \frac{x}{13841287201} ) ^{2}}{1384128720 1 ^{5}}

= 7^{17} - \frac{7 ^{16} \cdot 17 3 x}{3 13841287201} + 7^{15} \cdot 136 (3 \frac{x}{13841287201})^{2} - 33320 x + 16660 x 3 \frac{x}{13841287201} - \frac{6188 x 3 x ^{2}}{3 1384128720 1 ^{2}} + \frac{7 ^{11} \cdot 12376 x ^{2}}{1384128720 1 ^{2}} - \frac{19448 x ^{\frac{7}{3}}}{282475249 \cdot 1384128720 1 ^{\frac{2}{3}}} + \frac{980996186170 x ^{2} 3 x ^{2}}{1384128720 1 ^{2} 3 1384128720 1 ^{2}} - \frac{140142312310 x ^{3}}{1384128720 1 ^{3}} + \frac{6670664 x ^{\frac{10}{3}}}{1384128720 1 ^{3}} - \frac{1456024024 x ^{3} 3 x ^{2}}{1384128720 1 ^{3} 3 1384128720 1 ^{2}} + \frac{104001716 x ^{4}}{1384128720 1 ^{4}} - \frac{2380 x ^{\frac{13}{3}}}{1384128720 1 ^{4}} + \frac{233240 x ^{4} 3 x ^{2}}{1384128720 1 ^{4} 3 1384128720 1 ^{2}} - \frac{6664 x ^{5}}{1384128720 1 ^{5}} + \frac{17 x ^{\frac{16}{3}}}{1384128720 1 ^{5} \cdot 343} - \frac{x ^{5} ( 3 \frac{x}{13841287201} ) ^{2}}{1384128720 1 ^{5}}

7^{17} - \frac{7 ^{16} \cdot 17 3 x}{3 13841287201} + 7^{15} \cdot 136 (3 \frac{x}{13841287201})^{2} - 33320 x + 16660 x 3 \frac{x}{13841287201} - \frac{6188 x 3 x ^{2}}{3 1384128720 1 ^{2}} + \frac{7 ^{11} \cdot 12376 x ^{2}}{1384128720 1 ^{2}} - \frac{19448 x ^{\frac{7}{3}}}{282475249 \cdot 1384128720 1 ^{\frac{2}{3}}} + \frac{980996186170 x ^{2} 3 x ^{2}}{1384128720 1 ^{2} 3 1384128720 1 ^{2}} - \frac{140142312310 x ^{3}}{1384128720 1 ^{3}} + \frac{6670664 x ^{\frac{10}{3}}}{1384128720 1 ^{3}} - \frac{1456024024 x ^{3} 3 x ^{2}}{1384128720 1 ^{3} 3 1384128720 1 ^{2}} + \frac{104001716 x ^{4}}{1384128720 1 ^{4}} - \frac{2380 x ^{\frac{13}{3}}}{1384128720 1 ^{4}} + \frac{233240 x ^{4} 3 x ^{2}}{1384128720 1 ^{4} 3 1384128720 1 ^{2}} - \frac{6664 x ^{5}}{1384128720 1 ^{5}} + \frac{17 x ^{\frac{16}{3}}}{1384128720 1 ^{5} \cdot 343} - \frac{x ^{5} ( 3 \frac{x}{13841287201} ) ^{2}}{1384128720 1 ^{5}}

פשט את:

7^{17} - \frac{7 ^{16} \cdot 17 3 x}{3 13841287201} + 7^{15} \cdot 136 (3 \frac{x}{13841287201})^{2} - 33320 x + 16660 x 3 \frac{x}{13841287201} - \frac{6188 x 3 x ^{2}}{3 1384128720 1 ^{2}} + \frac{7 ^{11} \cdot 12376 x ^{2}}{1384128720 1 ^{2}} - \frac{19448 3 x ^{7}}{282475249 3 1384128720 1 ^{2}} + \frac{980996186170 x ^{2} 3 x ^{2}}{1384128720 1 ^{2} 3 1384128720 1 ^{2}} - \frac{140142312310 x ^{3}}{1384128720 1 ^{3}} + \frac{6670664 3 x ^{10}}{1384128720 1 ^{3}} - \frac{1456024024 x ^{3} 3 x ^{2}}{1384128720 1 ^{3} 3 1384128720 1 ^{2}} + \frac{104001716 x ^{4}}{1384128720 1 ^{4}} - \frac{2380 3 x ^{13}}{1384128720 1 ^{4}} + \frac{233240 x ^{4} 3 x ^{2}}{1384128720 1 ^{4} 3 1384128720 1 ^{2}} - \frac{6664 x ^{5}}{1384128720 1 ^{5}} + \frac{17 3 x ^{16}}{1384128720 1 ^{5} \cdot 343} - \frac{x ^{5} ( 3 \frac{x}{13841287201} ) ^{2}}{1384128720 1 ^{5}}

= 7^{17} - \frac{7 ^{16} \cdot 17 3 x}{3 13841287201} + 7^{15} \cdot 136 (3 \frac{x}{13841287201})^{2} - 33320 x + 16660 x 3 \frac{x}{13841287201} - \frac{6188 x 3 x ^{2}}{3 1384128720 1 ^{2}} + \frac{7 ^{11} \cdot 12376 x ^{2}}{1384128720 1 ^{2}} - \frac{19448 3 x ^{7}}{282475249 3 1384128720 1 ^{2}} + \frac{980996186170 x ^{2} 3 x ^{2}}{1384128720 1 ^{2} 3 1384128720 1 ^{2}} - \frac{140142312310 x ^{3}}{1384128720 1 ^{3}} + \frac{6670664 3 x ^{10}}{1384128720 1 ^{3}} - \frac{1456024024 x ^{3} 3 x ^{2}}{1384128720 1 ^{3} 3 1384128720 1 ^{2}} + \frac{104001716 x ^{4}}{1384128720 1 ^{4}} - \frac{2380 3 x ^{13}}{1384128720 1 ^{4}} + \frac{233240 x ^{4} 3 x ^{2}}{1384128720 1 ^{4} 3 1384128720 1 ^{2}} - \frac{6664 x ^{5}}{1384128720 1 ^{5}} + \frac{17 3 x ^{16}}{1384128720 1 ^{5} \cdot 343} - \frac{x ^{5} ( 3 \frac{x}{13841287201} ) ^{2}}{1384128720 1 ^{5}}

דוגמאות פופולריות

simplify \delta(x-40pi)

s im pl i f y δ (x - 40 π)

expand (1+x^{3/4})(1-x^{2/3})

e x p an d (1 + x^{\frac{3}{4}}) (1 - x^{\frac{2}{3}})

simplify (sqrt(x+\sqrt{y)}-sqrt(x-\sqrt{y)})^2

s im pl i f y (x + y - x - y)^{2}

expand (x^2-2x)frace^{2x}2

e x p an d (x^{2} - 2 x) f r a c e^{2 x} 2

expand tan(x)(tan(x)+1)

e x p an d tan (x) (tan (x) + 1)