Unit 6, Lesson 19
Expanding and Factoring
Grade 7
Practice
Problem 1
- Expand to write an equivalent expression: \(\frac {\text{-}1}{4}(\text-8x+12y)\)
- Factor to write an equivalent expression: \(36a-16\)
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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?
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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.
\(\displaystyle 75a + 25b = \underline{\ \ \ \ }( \underline{\ \ \ \ }a + b)\)
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Problem 4
Elena's favorite shade of purple paint can be made by mixing 3 cups of blue paint, \(1\frac12\) cups of red paint, and \(\frac{1}{2}\) cup of white paint. Elena has \(\frac{2}{3}\) 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 \(\frac{2}{3}\) cup of white paint?
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Problem 5
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 6
Select all the inequalities that have the same solutions as \(\text-4x<20\).
\(\text-x<5\)
\(4x>\text-20\)
\(4x < \text-20\)