Binomická věta
Urči pomocí binomické věty:
\large \left( x-y\right) ^6
\large{{6}\choose2{}}={{6}\choose4}=\frac{6!}{2!\cdot4!}=\frac{6\cdot5}{2}=15
\large{{6}\choose{3}}=\frac{6!}{3!\cdot3!}=\frac{6\cdot5\cdot4}{6}=20
\large x^6-6x^5y+15x^4y^2-20x^3y^3+15x^2y^4-6xy^5+y^6
\large{{6}\choose2{}}={{6}\choose4}=\frac{6!}{2!\cdot4!}=\frac{6\cdot5}{2}=14
\large{{6}\choose{3}}=\frac{6!}{3!\cdot3!}=\frac{6\cdot5\cdot4}{6}=20
\large x^6-6x^5y+15x^4y^2-20x^3y^3+15x^2y^4-6xy^5+y^6
\large{{6}\choose2{}}={{6}\choose4}=\frac{6!}{2!\cdot4!}=\frac{6\cdot5}{2}=15
\large{{6}\choose{3}}=\frac{6!}{3!\cdot3!}=\frac{6\cdot5\cdot4}{6}=21
\large x^6-6x^5y+15x^4y^2-20x^3y^3+15x^2y^4-6xy^5+y^6
\large{{6}\choose2{}}={{6}\choose4}=\frac{6!}{2!\cdot4!}=\frac{6\cdot5}{2}=15
\large{{6}\choose{3}}=\frac{6!}{3!\cdot3!}=\frac{6\cdot5\cdot4}{6}=20
\large x^6-6x^5y+15x^4y^2-20x^3y^3+14x^2y^4-6xy^5+y^6