Unit 4, Lesson 2
Expanding and Factoring
Accelerated 7
Practice
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 help Lin understand factoring?
Problem 3
Complete the equation with numbers that make 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.
\(\frac {\text{-}1}{8}a-4=\frac {\text{-}3}{8}\)
\(\frac {\text{-}1}{4}b+5=16\)
\(10c+\text-45=\text-43\)
\(\text-8(d-1.25)=4\)
\(3.2(e+10)=32\)
Problem 5
Select all the inequalities that have the same solutions as \(\text-4x<20\).
\(\text-x<5\)
\(4x>\text-20\)
\(4x < \text-20\)
\(x < \text-5\)
\(x>5\)
\(x>\text-5\)
Problem 6
Each row contains the degree measures of two complementary angles. Complete the table.
| measure of an angle | measure of its complement |
|---|---|
| \(80^\circ\) | |
| \(25^\circ\) | |
| \(54^\circ\) | |
| \(x\) |