해법
확장 (5−41220703125x)19
해법
519−4559⋅194x+517⋅171(41220703125x)2−516⋅969(41220703125x)3+96900x−58140x41220703125x+122070312527132x3−541220703125350388x4x3+3051757812575582x2−15258789062592378x241220703125x+1953125⋅6252122070312592378x5−390625⋅3125241220703125375582x24x3+53250388x3−156255⋅12527132x341220703125x+31255⋅1253122070312511628x7−6258⋅1254122070312533876x34x3+549969x4−2523⋅625171x441220703125x+551122070312519x9−12207031254x4(41220703125x)3
솔루션 단계
(5−41220703125x)19
이항 정리 적용: (a+b)n=i=0∑n(in)a(n−i)bia=5,b=−41220703125x
=i=0∑19(i19)⋅5(19−i)(−41220703125x)i
합계 확장
=0!(19−0)!19!⋅519(−41220703125x)0+1!(19−1)!19!⋅518(−41220703125x)1+2!(19−2)!19!⋅517(−41220703125x)2+3!(19−3)!19!⋅516(−41220703125x)3+4!(19−4)!19!⋅515(−41220703125x)4+5!(19−5)!19!⋅514(−41220703125x)5+6!(19−6)!19!⋅513(−41220703125x)6+7!(19−7)!19!⋅512(−41220703125x)7+8!(19−8)!19!⋅511(−41220703125x)8+9!(19−9)!19!⋅510(−41220703125x)9+10!(19−10)!19!⋅59(−41220703125x)10+11!(19−11)!19!⋅58(−41220703125x)11+12!(19−12)!19!⋅57(−41220703125x)12+13!(19−13)!19!⋅56(−41220703125x)13+14!(19−14)!19!⋅55(−41220703125x)14+15!(19−15)!19!⋅54(−41220703125x)15+16!(19−16)!19!⋅53(−41220703125x)16+17!(19−17)!19!⋅52(−41220703125x)17+18!(19−18)!19!⋅51(−41220703125x)18+19!(19−19)!19!⋅50(−41220703125x)19
0!(19−0)!19!⋅519(−41220703125x)0간소화하다 :519
1!(19−1)!19!⋅518(−41220703125x)1간소화하다 :−41220703125518⋅194x
2!(19−2)!19!⋅517(−41220703125x)2간소화하다 :517⋅171(41220703125x)2
3!(19−3)!19!⋅516(−41220703125x)3간소화하다 :−516⋅969(41220703125x)3
4!(19−4)!19!⋅515(−41220703125x)4간소화하다 :1220703125515⋅3876x
5!(19−5)!19!⋅514(−41220703125x)5간소화하다 :−514⋅11628(41220703125x)5
6!(19−6)!19!⋅513(−41220703125x)6간소화하다 :513⋅27132(41220703125x)6
7!(19−7)!19!⋅512(−41220703125x)7간소화하다 :−1.23018E13(41220703125x)7
8!(19−8)!19!⋅511(−41220703125x)8간소화하다 :122070312523690527343750x2
9!(19−9)!19!⋅510(−41220703125x)9간소화하다 :−902128906250(41220703125x)9
10!(19−10)!19!⋅59(−41220703125x)10간소화하다 :180425781250(41220703125x)10
11!(19−11)!19!⋅58(−41220703125x)11간소화하다 :−29524218750(41220703125x)11
12!(19−12)!19!⋅57(−41220703125x)12간소화하다 :122070312533936562500x3
13!(19−13)!19!⋅56(−41220703125x)13간소화하다 :−423937500(41220703125x)13
14!(19−14)!19!⋅55(−41220703125x)14간소화하다 :36337500(41220703125x)14
15!(19−15)!19!⋅54(−41220703125x)15간소화하다 :−2422500(41220703125x)15
16!(19−16)!19!⋅53(−41220703125x)16간소화하다 :12207031254121125x4
17!(19−17)!19!⋅52(−41220703125x)17간소화하다 :−4275(41220703125x)17
18!(19−18)!19!⋅51(−41220703125x)18간소화하다 :95(41220703125x)18
19!(19−19)!19!⋅50(−41220703125x)19간소화하다 :−(41220703125x)19
=519−41220703125518⋅194x+517⋅171(41220703125x)2−516⋅969(41220703125x)3+1220703125515⋅3876x−514⋅11628(41220703125x)5+513⋅27132(41220703125x)6−1.23018E13(41220703125x)7+122070312523690527343750x2−902128906250(41220703125x)9+180425781250(41220703125x)10−29524218750(41220703125x)11+122070312533936562500x3−423937500(41220703125x)13+36337500(41220703125x)14−2422500(41220703125x)15+12207031254121125x4−4275(41220703125x)17+95(41220703125x)18−(41220703125x)19
519−41220703125518⋅194x+517⋅171(41220703125x)2−516⋅969(41220703125x)3+1220703125515⋅3876x−514⋅11628(41220703125x)5+513⋅27132(41220703125x)6−1.23018E13(41220703125x)7+122070312523690527343750x2−902128906250(41220703125x)9+180425781250(41220703125x)10−29524218750(41220703125x)11+122070312533936562500x3−423937500(41220703125x)13+36337500(41220703125x)14−2422500(41220703125x)15+12207031254121125x4−4275(41220703125x)17+95(41220703125x)18−(41220703125x)19간소화하다 :519−5459⋅194x+517⋅171(41220703125x)2−516⋅969(41220703125x)3+96900x−58140x41220703125x+122070312527132x23−541220703125350388x4x3+3051757812575582x2−15258789062592378x241220703125x+1953125⋅6252122070312592378x25−390625⋅3125241220703125375582x24x3+53250388x3−156255⋅12527132x341220703125x+31255⋅1253122070312511628x27−6258⋅1254122070312533876x34x3+549969x4−2523⋅625171x441220703125x+551122070312519x29−12207031254x4(41220703125x)3
=519−5459⋅194x+517⋅171(41220703125x)2−516⋅969(41220703125x)3+96900x−58140x41220703125x+122070312527132x23−541220703125350388x4x3+3051757812575582x2−15258789062592378x241220703125x+1953125⋅6252122070312592378x25−390625⋅3125241220703125375582x24x3+53250388x3−156255⋅12527132x341220703125x+31255⋅1253122070312511628x27−6258⋅1254122070312533876x34x3+549969x4−2523⋅625171x441220703125x+551122070312519x29−12207031254x4(41220703125x)3
519−5459⋅194x+517⋅171(41220703125x)2−516⋅969(41220703125x)3+96900x−58140x41220703125x+122070312527132x23−541220703125350388x4x3+3051757812575582x2−15258789062592378x241220703125x+1953125⋅6252122070312592378x25−390625⋅3125241220703125375582x24x3+53250388x3−156255⋅12527132x341220703125x+31255⋅1253122070312511628x27−6258⋅1254122070312533876x34x3+549969x4−2523⋅625171x441220703125x+551122070312519x29−12207031254x4(41220703125x)3간소화하다 :519−4559⋅194x+517⋅171(41220703125x)2−516⋅969(41220703125x)3+96900x−58140x41220703125x+122070312527132x3−541220703125350388x4x3+3051757812575582x2−15258789062592378x241220703125x+1953125⋅6252122070312592378x5−390625⋅3125241220703125375582x24x3+53250388x3−156255⋅12527132x341220703125x+31255⋅1253122070312511628x7−6258⋅1254122070312533876x34x3+549969x4−2523⋅625171x441220703125x+551122070312519x9−12207031254x4(41220703125x)3
=519−4559⋅194x+517⋅171(41220703125x)2−516⋅969(41220703125x)3+96900x−58140x41220703125x+122070312527132x3−541220703125350388x4x3+3051757812575582x2−15258789062592378x241220703125x+1953125⋅6252122070312592378x5−390625⋅3125241220703125375582x24x3+53250388x3−156255⋅12527132x341220703125x+31255⋅1253122070312511628x7−6258⋅1254122070312533876x34x3+549969x4−2523⋅625171x441220703125x+551122070312519x9−12207031254x4(41220703125x)3
인기 있는 예
확장 (cos(2)(x-1))-1expand(cos(2)(x−1))−1확장 (1+tan(x)+sec(x))(1+cot(x)-csc(x))expand(1+tan(x)+sec(x))(1+cot(x)−csc(x))단순화 (h)(sqrt(2x+2h+6)+sqrt(2x+3))simplify(h)(2x+2h+6+2x+3)단순화 (sqrt(4-r^2)+sqrt(9-r^2))^2simplify(4−r2+9−r2)2확장 ((0.159+x)(0.1251+x))/((0.5612-x))expand(0.5612−x)(0.159+x)(0.1251+x)