Mathematik
Formelsammlung für Klassen der BF I
Klammerregeln:
| Aufgabe | Langform | Kurzform | Distributivgesetz | ||
| a*(b+c) | = | a*b + b*c | = | ab + cd | |
| (a+b)*c | = | a*c + a*c | = | ac + ac | |
| a*(3+b) | = | a*3 + a*b | = | 3a + ab | |
| 4*(5+a) | = | 4*5 + 4*a | = | 20 + 4a |
| Aufgabe | Langform | Kurzform | Assoziativgesetz | ||
| (a + b) + c | = | a + (c + b) | = | a+b+c | |
| (3 + a) + b | = | 3 + (a + b) | = | a+b+3 | |
| (a*b)*c | = | a*(b*c) | = | abc | |
| (3*a)*4 | = | 3*(a*4) | = | 12a |
Vertauschungsgesetz:
| Aufgabe | Langform | Kurzform | Kommutativgesetz | ||
| b + c | = | c + b | = | ||
| 3 + a | = | a + 3 | = | ||
| a*b | = | b*a | = | ab | |
| a*4 | = | 4*a | = | 4a | |
| 5*8 | = | 8*5 | = | 40 |
Klammern auflösen
| Aufgabe | Langform | Kurzform | |||
| -(a+b) | = | -1*(a+b) | = | -a-b | |
| -(a-b) | = | -1*(a-b) | = | -a+b | |
| -(-a-b) | = | -1*(-a-b) | = | a+b | |
| -3(a+b) | = | -3*(a+b) | = | -3a-3b | |
| -4(-a-b) | = | -4*(-a-b) | = | 4a+4b | |
| -4(3-4) | = | -4*(3-4) | = | 4 | |
| 12a(3a-a) | = | 12a*(3a-1a) | = | 24a2 | |
+ und * unterscheiden
| Aufgabe | Langform | Kurzform | ||
| a+a | = | 1*a+1*a | = | 2a |
| a*a | = | 1*a*1*a | = | a2 |
| a+a+a | = | 1*a+1*a+1*a | = | 3a |
| a*a*a | = | 1*a*1*a*1*a | = | a3 |
| a+a+b+b | = | 1*a+1*a+1*b+1*b | = | 2a+2b |
| aabb | = | a*a*b*b | = | a2b2 |
| abab | = | a*b*a*b | = | a2b2 |
| aa+bb | = | a*a+b*b | = | a2+b2 |
| ab+ab | = | a*b+a*b | = | 2ab |
| ab+ba | = | a*b+b*a | = | 2ab |
| a(b+b) | = | a*(b+b) | = | 2ab |
| b(a+a) | = | b*(a+a) | = | 2ab |
| (2b)a | = | (2*b)*a | = | 2ab |
| x+y+xy | = | x+y+x*y | = | x+y+xy |
| x+x2+x3+x4 | = | x+x2+x3+x4 |
| Aufgabe | Langform | Kurzform | ||
| 3xy+3x+3y+3yx | = | = | 6xy+3x+3y | |
| xy+yx+3xy-4yx | = | = | Lösung | |
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