Mit Hilfe des Pascalschen Dreiecks multiplizieren Sie die Klammern aus:
{\displaystyle \quad } A) ( a 3 − 4 ) 5 {\displaystyle \ \left(a^{3}-4\right)^{5}\quad } {\displaystyle \quad } B) ( 5 x 2 + 4 z 5 ) 4 {\displaystyle \ \left(5\ x^{2}+4\ z^{5}\right)^{4}\quad }
{\displaystyle \quad } A) ( a 3 − 4 ) 5 = {\displaystyle \ \left(a^{3}-4\right)^{5}=} {\displaystyle \quad } 1 ⋅ ( a 3 ) 5 4 0 1 − 5 ⋅ ( a 3 ) 4 4 1 + 1 0 ⋅ ( a 3 ) 3 4 2 − 1 0 ⋅ ( a 3 ) 2 4 3 + 5 ⋅ ( a 3 ) 1 4 4 − 1 ⋅ ( a 3 ) 0 1 4 5 {\displaystyle {\color {red}\mathbf {1} }\cdot \left(a^{3}\right)^{5}\ {\cancelto {1}{\ 4^{0}\ }}-{\color {red}\mathbf {5} }\cdot \left(a^{3}\right)^{4}\ 4^{1}+{\color {red}\mathbf {1} 0}\cdot \left(a^{3}\right)^{3}\ 4^{2}-{\color {red}\mathbf {1} 0}\cdot \left(a^{3}\right)^{2}\ 4^{3}+{\color {red}\mathbf {5} }\cdot \left(a^{3}\right)^{1}\ 4^{4}-{\color {red}\mathbf {1} }\cdot {\cancelto {1}{\ \left(a^{3}\right)^{0}\ }}\ 4^{5}} {\displaystyle \quad } a 15 − 20 ⋅ a 12 + 160 ⋅ a 9 − 640 ⋅ a 6 + 1280 ⋅ a 3 − 1024 {\displaystyle a^{15}\ -20\cdot a^{12}\ +160\cdot a^{9}\ -640\cdot a^{6}\ +1280\cdot a^{3}\ -1024\ } {\displaystyle \quad } B) ( 5 x 2 + 4 z 5 ) 4 = {\displaystyle \ \left(5\ x^{2}+4\ z^{5}\right)^{4}=\quad } {\displaystyle \quad } 1 ⋅ ( 5 x 2 ) 4 ( 4 z 5 ) 0 1 + 4 ⋅ ( 5 x 2 ) 3 ( 4 z 5 ) 1 + 6 ⋅ ( 5 x 2 ) 2 ( 4 z 5 ) 2 + 4 ⋅ ( 5 x 2 ) 1 ( 4 z 5 ) 3 + 1 ⋅ ( 5 x 2 ) 0 1 ( 4 z 5 ) 4 {\displaystyle {\color {red}\mathbf {1} }\cdot \left(5\ x^{2}\right)^{4}\ {\cancelto {1}{\ \left(4\ z^{5}\right)^{0}\ }}+{\color {red}\mathbf {4} }\cdot \left(5\ x^{2}\right)^{3}\ \left(4\ z^{5}\right)^{1}+{\color {red}\mathbf {6} }\cdot \left(5\ x^{2}\right)^{2}\ \left(4\ z^{5}\right)^{2}+{\color {red}\mathbf {4} }\cdot \left(5\ x^{2}\right)^{1}\ \left(4\ z^{5}\right)^{3}+{\color {red}\mathbf {1} }\cdot {\cancelto {1}{\ \left(5\ x^{2}\right)^{0}\ }}\ \left(4\ z^{5}\right)^{4}} {\displaystyle \quad } 625 ⋅ x 8 z 5 + 2000 ⋅ x 6 z 10 + 2400 ⋅ x 4 z 15 1280 ⋅ x 2 z 20 + 256 ⋅ z 25 {\displaystyle 625\cdot x^{8}\ z^{5}\ +2000\cdot x^{6}\ z^{10}\ +2400\cdot x^{4}\ z^{15}\ 1280\cdot x^{2}\ z^{20}\ +256\cdot z^{25}\ \ }
