# 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.

1. $$(30 + 3)(30 - 2)$$
2. $$(20 - 1)(20 -1)$$
3. $$(100 + 5)(100 - m)$$
4. $$(40 - a)(40 + b)$$
5. $$y(11-y)$$
6. $$\text-7(3a-1)$$
7. $$\frac14 (\text-8a + 12a)$$
8. $$\text-x(3x-5)$$

### 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
$$\text-3(5-2y)$$ $$\text-15+6y$$
$$c(c-5)$$
$$8a-4b$$
$$\text-3(2w-7z)$$
$$\text-(3y-2x)$$
$$12x-14x^2$$
$$n(3-10)$$
$$5y-7y$$
$$\text-5x(y-2z)$$
$$wt-tv-5tz$$
$$\text-a(2b-4c+a)$$