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1. Binomische Formel Aufgaben mit Lösungen

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

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Lösungen

Aufgabe 1:
(6x + 8y)2 = 36x2 + 96xy + 64y2

a = 6xa2 = (6x)2 = 36x2
a = 8ya2 = (8y)2 = 64y2
ab = 6x·8y = 48xy2ab = 2 ·48xy = 96xy

Aufgabe 2:
(8x + 7y)2 = 64x2 + 112xy + 49y2

a = 8xa2 = (8x)2 = 64x2
a = 7ya2 = (7y)2 = 49y2
ab = 8x·7y = 56xy2ab = 2 ·56xy = 112xy

Aufgabe 3:
(1x + 2y)2 = 1x2 + 4xy + 4y2

a = 1xa2 = (1x)2 = 1x2
a = 2ya2 = (2y)2 = 4y2
ab = 1x·2y = 2xy2ab = 2 ·2xy = 4xy

Aufgabe 4:
(5x + 7y)2 = 25x2 + 70xy + 49y2

a = 5xa2 = (5x)2 = 25x2
a = 7ya2 = (7y)2 = 49y2
ab = 5x·7y = 35xy2ab = 2 ·35xy = 70xy

Aufgabe 5:
(6x + 7y)2 = 36x2 + 84xy + 49y2

a = 6xa2 = (6x)2 = 36x2
a = 7ya2 = (7y)2 = 49y2
ab = 6x·7y = 42xy2ab = 2 ·42xy = 84xy

Aufgabe 6:
(7x + 7y)2 = 49x2 + 98xy + 49y2

a = 7xa2 = (7x)2 = 49x2
a = 7ya2 = (7y)2 = 49y2
ab = 7x·7y = 49xy2ab = 2 ·49xy = 98xy

Aufgabe 7:
(7x + 10y)2 = 49x2 + 140xy + 100y2

a = 7xa2 = (7x)2 = 49x2
a = 10ya2 = (10y)2 = 100y2
ab = 7x·10y = 70xy2ab = 2 ·70xy = 140xy

Aufgabe 8:
(10x + 8y)2 = 100x2 + 160xy + 64y2

a = 10xa2 = (10x)2 = 100x2
a = 8ya2 = (8y)2 = 64y2
ab = 10x·8y = 80xy2ab = 2 ·80xy = 160xy

Aufgabe 9:
(5x + 4y)2 = 25x2 + 40xy + 16y2

a = 5xa2 = (5x)2 = 25x2
a = 4ya2 = (4y)2 = 16y2
ab = 5x·4y = 20xy2ab = 2 ·20xy = 40xy

Aufgabe 10:
(6x + 2y)2 = 36x2 + 24xy + 4y2

a = 6xa2 = (6x)2 = 36x2
a = 2ya2 = (2y)2 = 4y2
ab = 6x·2y = 12xy2ab = 2 ·12xy = 24xy

Aufgabe 11:
(3x + 1y)2 = 9x2 + 6xy + 1y2

a = 3xa2 = (3x)2 = 9x2
a = 1ya2 = (1y)2 = 1y2
ab = 3x·1y = 3xy2ab = 2 ·3xy = 6xy

Aufgabe 12:
(5x + 2y)2 = 25x2 + 20xy + 4y2

a = 5xa2 = (5x)2 = 25x2
a = 2ya2 = (2y)2 = 4y2
ab = 5x·2y = 10xy2ab = 2 ·10xy = 20xy

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