# Lesson 19

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

Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, \(1\frac12\) cups of red paint, and \(\frac{1}{2}\) of a cup of white paint. Elena has \(\frac{2}{3}\) of a cup of white paint.

- Assuming she has enough red paint and blue paint, how much purple paint can Elena make?
- How much blue paint and red paint will Elena need to use with the \(\frac{2}{3}\) of a cup of white paint?

### Problem 5

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 6

Select** all** the inequalities that have the same solutions as \(\text-4x<20\).

\(\text-x<5\)

\(4x>\text-20\)

\(4x < \text-20\)

\(x < \text-5\)

\(x>5\)

\(x>\text-5\)