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Klasse
9 - Termumformung |
erarbeitet von R. Bothe |
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1. |
Löse die Klammern auf und fasse zusammen. |
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a) |
3x - 4 × (3x - 4) |
= -9x + 16 |
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b) |
(3x - 4) × (3x + 4) |
= 9x2
- 16 |
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c) |
- (3x - 4) - (3x - 4) |
= -6x + 8 |
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d) |
(3x - 4) × 3x - 4 |
= 9x2
–12x – 4 |
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e) |
(3x - 4) + (3x - 4) |
= 6x - 8 |
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f) |
4x - (3x + 1)(3x - 1) |
= -9x2 +´4x + 1 |
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g) |
(3x - 4)2 - (3x + 4)2 |
= -48x |
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h) |
3x - [4x - (x + 1)(x - 3) +4] |
= x2 – 3x – 7 |
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2. |
Forme radikal in Produkte um. |
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a) |
4x3 - 16x2 + 16x |
= 4x (x - 2)2 |
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b) |
x3 + 5x2 + 25x |
= x (x2 + 5x + 25) |
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c) |
4x2 - 36 |
= 4 (x - 3)(x + 3) |
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d) |
3x3 + 6x2 - 2x - 4 |
= (x + 2)(3x2
- 2) |
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e) |
x3 + 3·x2 - 4 |
= (x - 1)(x + 2)2 |
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f) |
x4
- 8x2 + 16 |
= (x - 2)2 × (x + 2)2 |
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3. |
Forme in sinnvoll in Summen um. |
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a) |
(4x5 - 3x4 + 4x3 - 5) : x3 |
= 4x2 - 3x + 4 - 5/x3 |
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b) |
(4x3 - 3x2 + 4x - 5) : (x - 1) |
= 4x2 + x + 5 |
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c) |
(4x3 + 3x - 4) : (2x - 1) |
= 4x2 + x + 2 - 2/(2x - 1) |
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4. |
Forme in Quotienten um. |
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