Aufgaben
Wende auf die Aufgaben die erste binomische Formel an.
Aufgabe 1:
(6x + 8y)
2
Aufgabe 2:
(8x + 7y)
2
Aufgabe 3:
(1x + 2y)
2
Aufgabe 4:
(5x + 7y)
2
Aufgabe 5:
(6x + 7y)
2
Aufgabe 6:
(7x + 7y)
2
Aufgabe 7:
(7x + 10y)
2
Aufgabe 8:
(10x + 8y)
2
Aufgabe 9:
(5x + 4y)
2
Aufgabe 10:
(6x + 2y)
2
Aufgabe 11:
(3x + 1y)
2
Aufgabe 12:
(5x + 2y)
2
Lösungen
Aufgabe 1:
(6x + 8y)
2 = 36x
2 + 96xy + 64y
2
a = 6x | a2 = (6x)2 = 36x2 |
a = 8y | a2 = (8y)2 = 64y2 |
ab = 6x·8y = 48xy | 2ab = 2 ·48xy = 96xy |
Aufgabe 2:
(8x + 7y)
2 = 64x
2 + 112xy + 49y
2
a = 8x | a2 = (8x)2 = 64x2 |
a = 7y | a2 = (7y)2 = 49y2 |
ab = 8x·7y = 56xy | 2ab = 2 ·56xy = 112xy |
Aufgabe 3:
(1x + 2y)
2 = 1x
2 + 4xy + 4y
2
a = 1x | a2 = (1x)2 = 1x2 |
a = 2y | a2 = (2y)2 = 4y2 |
ab = 1x·2y = 2xy | 2ab = 2 ·2xy = 4xy |
Aufgabe 4:
(5x + 7y)
2 = 25x
2 + 70xy + 49y
2
a = 5x | a2 = (5x)2 = 25x2 |
a = 7y | a2 = (7y)2 = 49y2 |
ab = 5x·7y = 35xy | 2ab = 2 ·35xy = 70xy |
Aufgabe 5:
(6x + 7y)
2 = 36x
2 + 84xy + 49y
2
a = 6x | a2 = (6x)2 = 36x2 |
a = 7y | a2 = (7y)2 = 49y2 |
ab = 6x·7y = 42xy | 2ab = 2 ·42xy = 84xy |
Aufgabe 6:
(7x + 7y)
2 = 49x
2 + 98xy + 49y
2
a = 7x | a2 = (7x)2 = 49x2 |
a = 7y | a2 = (7y)2 = 49y2 |
ab = 7x·7y = 49xy | 2ab = 2 ·49xy = 98xy |
Aufgabe 7:
(7x + 10y)
2 = 49x
2 + 140xy + 100y
2
a = 7x | a2 = (7x)2 = 49x2 |
a = 10y | a2 = (10y)2 = 100y2 |
ab = 7x·10y = 70xy | 2ab = 2 ·70xy = 140xy |
Aufgabe 8:
(10x + 8y)
2 = 100x
2 + 160xy + 64y
2
a = 10x | a2 = (10x)2 = 100x2 |
a = 8y | a2 = (8y)2 = 64y2 |
ab = 10x·8y = 80xy | 2ab = 2 ·80xy = 160xy |
Aufgabe 9:
(5x + 4y)
2 = 25x
2 + 40xy + 16y
2
a = 5x | a2 = (5x)2 = 25x2 |
a = 4y | a2 = (4y)2 = 16y2 |
ab = 5x·4y = 20xy | 2ab = 2 ·20xy = 40xy |
Aufgabe 10:
(6x + 2y)
2 = 36x
2 + 24xy + 4y
2
a = 6x | a2 = (6x)2 = 36x2 |
a = 2y | a2 = (2y)2 = 4y2 |
ab = 6x·2y = 12xy | 2ab = 2 ·12xy = 24xy |
Aufgabe 11:
(3x + 1y)
2 = 9x
2 + 6xy + 1y
2
a = 3x | a2 = (3x)2 = 9x2 |
a = 1y | a2 = (1y)2 = 1y2 |
ab = 3x·1y = 3xy | 2ab = 2 ·3xy = 6xy |
Aufgabe 12:
(5x + 2y)
2 = 25x
2 + 20xy + 4y
2
a = 5x | a2 = (5x)2 = 25x2 |
a = 2y | a2 = (2y)2 = 4y2 |
ab = 5x·2y = 10xy | 2ab = 2 ·10xy = 20xy |