Terme am Würfelturm

Sichtbare Quadrate
[b]Ein Würfel liegt auf dem Tisch. Du kannst ihn von den 4 Seiten und von oben betrachten. Das Quadrat am Tisch ist verdeckt.[br][br][/b]Zähle die sichtbaren Quadrate.
[b]Du kannst den Schieberegler betätigen und dir die ersten 10 Stockwerke betrachten.[br][/b] [br] [br]
Tabelle für die Anzahl der sichtbaren Quadrate
Stelle dir nun x-beliebige Stockwerke vor: gib die Anzahl der sichtbaren Quadrate mit Hilfe eines Terms an (Tipp: x steht für die Anzahl der Stockwerke).[br][br]Ergänze die Tabelle im Heft. 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Terme zusammenfassen

[br] [br] [br]Löse die Learning-App und übernimm den Text am Ende der LearningApp als Hefteintrag mit der Überschrift: [br][b][u]Terme zusammenfassen[/u][/b]
Übung:
Übernimm die Terme in dein Heft und vereinfache durch Zusammenfassen gleichartiger Terme. ([math]x,y,a\in\mathbb{Q}[/math])[br][br]a) 13x + 6 – 7x [br][br]b) 14a + 2 – 2a[br][br]c) –12x + 12 – 3x[br][br]d) 7 + 3y – 2y[br][br]e) 4x – x + 4 [br][br]f) 15a + 2 – 2a[br] [br]g) 4x – 3x + 5 – x

Terme multiplizieren (verschiedene Variablen und höhere Potenzen)

Terme multiplizieren beim Berechnen des Quadervolumens:
Aufgabe 1:
[b]a) Übernimm das Schrägbild des Quaders in dein Heft.[br]b) Erstelle einen Term (mit x) für das Volumen des Quaders ([/b][math]x\in\mathbb{Q}[/math][b]).[/b]
Aufgabe 2:
Aufgabe 3:
Übernimm die Terme in dein Heft und vereinfache. ([math]x,y,a,b\in \mathbb{Q}[/math])[br][br]a) [math]7x\cdot3xy[/math][br][br]b) [math]12ab^2\cdot\frac{1}{2}a[/math][br][br]c) [math]\left(2b\right)^2\cdot2b^2[/math][br][br]d) [math]3x^2\cdot\left(-2y\right)^3\cdot x^{-4}\cdot y^6\cdot\left(-a\right)[/math]

Plusklammer und Minusklammer

Beispiel 1:
[size=200][color=#0000ff][b]7 + (+3 – 8) = [/b][/color][/size][br][br]Welchen Rechenweg würdest du wählen?
[br] [br][b][size=100][size=150]Die Klammer in der Aufgabe heißt Plusklammer, weil vor der Klammer ein Plus steht![/size][/size][/b][br][br][img]data:image/png;base64,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[/img][br][br][b][size=150]Die Plusklammer wird weggelassen. Die Zeichen in der Klammer bleiben gleich.[br][br][/size][/b]Rechenweg 1 ist also richtig: 7 [b]+ ([/b][color=#ff00ff]+3 – 8[/color][b])[/b] = 7 [color=#ff00ff]+ 3 – 8[/color] = 10 – 8 = 2[br][br]Rechenweg 2 ist ebenfalls richtig: 7 + (+3 – 8) = 7 [b]+ ([/b][color=#ff00ff]–5[/color][b]) [/b]= 7 [color=#ff00ff]– 5[/color] = 2[br] [br] [br] [br] [br] [br]
Beispiel 2:
[size=200][color=#0000ff][b]12 [b]–[/b] (+2 – 5) = [/b][/color][/size][br][br]Welchen Rechenweg würdest du wählen?
[br] [br][b][size=100][size=150]Die Klammer in der Aufgabe heißt Minusklammer, weil vor der Klammer ein Minus steht![/size][/size][/b][br][br][img]data:image/png;base64,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[/img][br][br][b][size=150]Die Minusklammer wird weggelassen. Die Zeichen in der Klammer werden umgekehrt.[br][br][/size][/b]Rechenweg 1 ist also richtig: 12 [b]– ([/b][color=#ff7700]+2 – 5[/color][b])[/b] = 12 [color=#ff7700]– 2 + 5[/color] = 10 + 5 = 15[br][br]Rechenweg 2 ist ebenfalls richtig: 12 – (+2 – 5) = 12 [b]– ([/b][color=#ff7700]–3[/color][b])[/b] = 12 [color=#ff7700]+ 3[/color] = 15[br] [br] [br] [br] [br] [br]
Übung:
Löse die Klammern auf und fasse zusammen.[br][br]a) 23 + (+7 – 11) [br][br]b) 6 – (–8 + 2)[br][br]c) 10 + (3 – 7)[br][br]d) –5 – (8 – 2)[br][br]e) 2 + (5 + x)[br][br]f) 15 – (–6 – x)[br][br]g) 7x – (9y + 3x)[br][br]h) 8x + (–2x + y)

Ausmultiplizieren

x-beliebige 10er-Stelle:
[size=150] [br]Die 10er-Stelle soll nun eine [color=#0000ff]x-beliebige Zahl[/color] sein. ([math]x\in\mathbb{N}; x<10[/math])[br] [br][br]Wir können den Term dann so schreiben: [/size] [size=200][b]7 · ([color=#0000ff]x[/color]+[color=#ff0000]3[/color])[br][/b][/size] [br] [br]Notiere die richtige Termumformung im Heft: [b]7 · (x + 3) = ...[/b]
Übung
Multipliziere aus. ([math]x\in\mathbb{Q}[/math])[br][br]a) 5 · (x + 6) =[br][br]b) 15 · (2 + x) =[br][br]c) x · (8 + x) =[br][br]d) 9 · (x – 6) =[br][br]e) –2 · (4 – x) =

Information