Expanding and Factoring


Activity #1

 Write Equivalent Expressions.

  • In each row in the table below, write the equivalent expression.
  • If you get stuck, use the diagram in the applet below to organize your work. The first row is provided as an example.

The diagrams below are provided for the first three rows.

Activity #2

 Explain What Expanding and Factoring Mean. 

  • Read the story below and attempt to explain the process of factoring to Lin who missed the class.

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.

(1.) How can Kiran explain factoring to Lin?

(2.) Lin asks Kiran how the diagrams with boxes help with factoring. What should Kiran tell Lin about the boxes?

(3.) Lin asks Kiran to help her factor the expression  How can Kiran use this example to Lin understand factoring?

Activity #3

 Practice Equivalent Expressions.

  • Do as many generated problems as possible to master expansion of algebraic expressions.
  • Make sure you attempt a problem first before you check on the answer.
  • Then click to do more problems.

Challenge #1

Challenge #2

Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint,  cups of red paint, and  of a cup of white paint. Elena has  of a cup of white paint.

(1.) Assuming she has enough red paint and blue paint, how much purple paint can Elena make?

(2.) How much blue paint and red paint will Elena need to use with the  of a cup of white paint?

Challenge #3

Expand the following to create an equivalent expression that uses the fewest number of terms:

If we wrote a new expression following the same pattern so that there were 20 sets of parentheses, how could it be expanded into an equivalent expression that uses the fewest number of terms? 

Quiz Time