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Expanding and factoring out

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

How do you calculate \(3 \cdot 12\) in your head? Maybe like this: \(3 \cdot 10 + 3 \cdot 2\). You do exactly the same with brackets in terms.
📄 Open worksheet (PDF, German)

The video

In the video we split a rectangle into two parts. This shows why \(3 \cdot (x + 2) = 3x + 6\).

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:24 The rectangle
  3. 0:43 Expanding
  4. 1:23 Factoring out
  5. 1:52 Careful, mistake!
  6. 2:14 Try it yourself

The most important points

A rectangle is 3 high and \(x + 2\) wide. Its area is \(3 \cdot (x + 2)\) or \(3x + 6\).

3 high, x + 2 wide: area 3 · (x + 2).
3 high, \(x + 2\) wide: area \(3 \cdot (x + 2)\).

Expanding (ausmultiplizieren)

The number in front of the bracket is multiplied by each part in the bracket: \(4 \cdot (2a - 5) = 8a - 20\).

With minus: -2 · (x + 3) = -2x - 6.
With minus: \(-2 \cdot (x + 3) = -2x - 6\).

Factoring out (ausklammern)

Factoring out is the way back. Look for the common factor: \(6x + 9 = 3 \cdot (2x + 3)\).

6 and 9 can both be divided by 3.
6 and 9 can both be divided by 3.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/3
The worksheet – Page 2
Page 2/3
Show the worksheet solutions
The worksheet – Page 3
Page 3/3

Try it yourself

Task

a) Expand: \(5 \cdot (x + 4)\) and \(2 \cdot (3y - 1)\). b) Factor out: \(4x + 8\).

Show solution

a) \(5x + 20\) and \(6y - 2\) b) \(4 \cdot (x + 2)\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Ausmultiplizieren und Ausklammern (Distributivgesetz, auch mit Minus). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.