# Lesson 8

Expanding and Factoring

Let's use the distributive property to write expressions in different ways.

### Problem 1

- Expand to write an equivalent expression: \(\frac {\text{-}1}{4}(\text-8x+12y)\)
- Factor to write an equivalent expression: \(36a-16\)

### Problem 2

Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up.

- Lin understands that expanding is using the distributive property, but she doesn’t understand what factoring is or why it works. How can Kiran explain factoring to Lin?
- Lin asks Kiran how the diagrams with boxes help with factoring. What should Kiran tell Lin about the boxes?
- Lin asks Kiran to help her factor the expression \(\text-4xy-12xz+20xw\). How can Kiran use this example to Lin understand factoring?

### Problem 3

Complete the equation with numbers that makes the expression on the right side of the equal sign equivalent to the expression on the left side.

\(\displaystyle 75a + 25b = \underline{\ \ \ \ }( \underline{\ \ \ \ }a + b)\)

### Problem 4

Solve each equation.

- \(\frac {\text{-}1}{8}d-4=\frac {\text{-}3}{8}\)
- \(\frac {\text{-}1}{4}m+5=16\)
- \(10b+\text-45=\text-43\)
- \(\text-8(y-1.25)=4\)
- \(3.2(s+10)=32\)

### Problem 5

For each inequality, decide whether the solution is represented by \(x < 4.5\) or \(x > 4.5\).

- \(\text-24>\text-6(x-0.5)\)
- \(\text-8x + 6 > \text-30\)
- \(\text-2(x + 3.2) < \text-15.4\)