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a) Vereinfachen sie so weit wie mōglich. \[ 12 b-[(2 a+4 b)-6 b]-[8 c-(8 b-a)]= \]

Ask by Osborne Schneider. in Switzerland
Mar 14,2025

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\[ 22b - 3a - 8c \]

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Um den gegebenen Ausdruck zu vereinfachen, schauen wir uns die inneren Klammern zuerst an: \[ 12 b - [(2 a + 4 b) - 6 b] - [8 c - (8 b - a)] \] Für die erste Klammer: \[ (2 a + 4 b) - 6 b = 2 a + 4 b - 6 b = 2 a - 2 b \] Für die zweite Klammer: \[ 8 c - (8 b - a) = 8 c - 8 b + a \] Nun setzen wir die Ergebnisse zurück in den Ausdruck: \[ 12 b - (2 a - 2 b) - (8 c - 8 b + a) \] Das vereinfacht sich zu: \[ 12 b - 2 a + 2 b - 8 c + 8 b - a \] Fassen wir die ähnlichen Terme zusammen: \[ (12 b + 2 b + 8 b) - (2 a + a) - 8 c = 22 b - 3 a - 8 c \] Der vereinfachte Ausdruck ist also: \[ 22 b - 3 a - 8 c \]

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