# Lesson 9

Working with Signed Numbers

- Let’s work with signed numbers.

### 9.1: Sorting Expressions

Sort these into two groups, so that the expressions in each group all have the same value.

- \(3-5\)
- \(5+3\)
- \(4 \boldcdot 2\)
- \(\text- \frac13 \boldcdot 6\)
- \(5 - \text-3\)
- \(\text-4 \boldcdot \text-2\)
- \(3 + \text-5\)
- \(\frac13 \boldcdot \text-6\)

### 9.2: Expanded Form

For each expression given in factored form, write two equivalent expressions in expanded form. If you get stuck, draw a diagram to represent the product. Some blank diagrams are provided—draw additional diagrams as needed.

- \((30 + 3)(30 - 2)\)
- \((20 - 1)(20 -1)\)
- \((100 + 5)(100 - m)\)
- \((40 - a)(40 + b)\)
- \(y(11-y)\)
- \(\text-7(3a-1)\)
- \(\frac14 (\text-8a + 12a)\)
- \(\text-x(3x-5)\)

### 9.3: Factoring and Expanding

In each row, write the equivalent expression. If you get stuck, use a diagram to organize your work. The first row is provided as an example. Diagrams are provided for the first three rows.

factored | expanded |
---|---|

\(\text-3(5-2y)\) | \(\text-15+6y\) |

\(c(c-5)\) | |

\(8a-4b\) | |

\(\text-3(2w-7z)\) | |

\(\text-(3y-2x)\) | |

\(12x-14x^2\) | |

\(n(3-10)\) | |

\(5y-7y\) | |

\(\text-5x(y-2z)\) | |

\(wt-tv-5tz\) | |

\(\text-a(2b-4c+a)\) |