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WP-MA: Klasse 9 – Umformen
von Summen in Produkte |
erarbeitet von R. Bothe |
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| Aufgabenübersicht - WP | Aufgabe | Lösungswege | |
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Ergebnisse: |
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Forme die folgenden Summen in Produkte um |
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a) |
14x3 + 7x2 + 21 x |
= |
7x × (2x2 + x + 3) |
Hilfe: Ausklammern B1 |
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b) |
9y2 + 3y2x - 6yx2 |
= |
3y × (3y + xy - 2x2) |
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c) |
3 × (a + b) + a2
× (a + b) |
= |
(a + b) × (3 + a2) |
Hilfe: Ausklammern B2 |
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d) |
(3x - 2)2 - 3ax + 2a |
= |
(3x - 2) × (3x - 2 - a) |
Hilfe: Mehrfachausklammern |
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e) |
9x3
+ 6x2 + 21x +14 |
= |
(3x + 2) × (3x2 + 7) |
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f) |
9m2
- 12m + 4 |
= |
(3m - 2)2 |
Hilfe: 1. binomische Formel |
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g) |
e2 +
8ex + 16x2 |
= |
(e + 4x)2 |
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h) |
k2 - 9 |
= |
(k + 3)(k - 3) |
Hilfe: 2. binomische Formel |
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i) |
k4 - 16 |
= |
(k2
+ 4)(k + 2)(k - 2) |
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j) |
9x2 - 4y2 |
= |
(3x + 2y)(3x - 2y) |
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k) |
2x2 - 20x +50 |
= |
2(x - 5)2 |
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l) |
b2 × (a + b ) - a2 × (a + b) |
= |
- (a + b)2 × (a - b) |
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m) |
(x + 3 )2 + 4x3 + 12x2 |
= |
(x + 3)(4x2 + x + 3) |
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n) |
x2 × (x - 3) - 4x +12 |
= |
(x - 3)(x + 2)(x - 2) |
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o) |
x4 - 4x3 - 2x2 + 8x |
= |
x(x - 4)(x + Ö2)(x - Ö2) |
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p) |
x2
- 6x - 16 |
= |
(x + 2)(x - 8) |
Hilfe : 1. + 2. binomische Formel |
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q) |
x3 +
4x2 - 5x |
= |
x × (x + 5)(x - 1) |
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r) |
x4 + 5x2 + 6 |
= |
(x2 + 3)(x2 + 2) |
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