Faktorisieren Sie folgende binomische Formeln:
{\displaystyle \quad } A) 169 a 8 − 52 a 4 + 4 {\displaystyle \ 169\ a^{8}-52\ a^{4}+4\qquad } {\displaystyle \qquad } B) 81 x 4 + 180 x 2 z 4 , 5 + 100 z 9 {\displaystyle \ 81\ x^{4}+180\ x^{2}\ z^{4{,}5}+100\ z^{9}\quad } {\displaystyle \quad } C) 49 w 7 + 70 w 10 + 25 w 13 {\displaystyle \ 49\ w^{7}+70\ w^{10}+25\ w^{13}\quad } {\displaystyle \quad } D) 9 c 4 − 49 b 10 {\displaystyle \ 9\ c^{4}-49\ b^{10}\quad } {\displaystyle \quad } E) 25 a 6 − 2 a 7 {\displaystyle \ 25\ a^{6}-2\ a^{7}\quad }
{\displaystyle \quad } A) 169 a 8 − 52 a 4 + 4 = ( 13 a 4 − 2 ) 2 {\displaystyle \ 169\ a^{8}-52\ a^{4}+4=\left(13\ a^{4}-2\right)^{2}} {\displaystyle \quad } B) 81 x 4 + 180 x 2 z 4 , 5 + 100 z 9 = ( 9 x 2 + 10 z 4 , 5 ) 2 {\displaystyle \ 81\ x^{4}+180\ x^{2}\ z^{4{,}5}+100\ z^{9}=\left(9\ x^{2}+10\ z^{4{,}5}\right)^{2}\quad } {\displaystyle \quad } C) 49 w 7 + 70 w 10 + 25 w 13 = ( 7 w 3 , 5 + 5 w 6 , 5 ) 2 {\displaystyle \ 49\ w^{7}+70\ w^{10}+25\ w^{13}=\left(7\ w^{3{,}5}+5\ w^{6{,}5}\right)^{2}\quad } {\displaystyle \quad } D) 9 c 4 − 49 b 10 = ( 3 c 2 − 7 b 5 ) ( 3 c 2 + 7 b 5 ) {\displaystyle \ 9\ c^{4}-49\ b^{10}=(3\ c^{2}-7\ b^{5})(3\ c^{2}+7\ b^{5})\quad } {\displaystyle \quad } E) 25 a 6 − 2 a 7 = ( 5 a 3 + 2 a 3 , 5 ) ( 5 a 3 − 2 a 3 , 5 ) {\displaystyle \ 25\ a^{6}-2\ a^{7}=(5\ a^{3}+{\sqrt {2}}\ a^{3{,}5})(5\ a^{3}-{\sqrt {2}}\ a^{3{,}5})\quad }
