Factoring Expressions

Examples, videos, and solutions to help Grade 6 students model and write equivalent expressions using the distributive property. They move from an expanded form to a factored form of an expression.

New York State Common Core Math Grade 6, Module 4, Lesson 11

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The following diagram uses models to show factoring expressions. Scroll down the page for more examples and solutions.

 

Learn how to factor expressions.

Example 1
a. Use the model to answer the following questions.
How many fives are in the model?
How many threes are in the model?
What does the expression represent in words?
What expression could we write to represent the model?
b. Use the new model and the previous model to answer the next set of questions.
How many fives are in the model?
How many threes are in the model?
What does the expression represent in words?
What expression could we write to represent the model?
c. Is the model in part (a) equivalent to the model in part (b)?
d. What relationship do we see happening on either side of the equal sign?
e. In 5th grade and in Module 2 of this year, you have used similar reasoning to solve problems. What is the name of the property that is used to say that 2(5 + 3) is the same as 2 x 5 + 2 x 3?

Example 2
Now, we will take a look at an example with variables.
What does the model represent in words?
What does 2a mean?
How many a’s are in the model?
How many b’s are in the model?
What expression could we write to represent the model?
How many a’s are in the expression?
How many b’s are in the expression?
What expression could we write to represent the model?

Example 3
Use GCF and the distributive property to write equivalent expressions.

1. 3f + 3g
   
2. 6x + 9y
   
3. 3c + 11c
   
4. 24b + 8
   

Exercises

1. Apply the distributive property to write equivalent expressions.
   a. 7x + 7y
   b. 15g + 20h
   c. 18m + 42n
   d. 30a + 39b
   e. 11f + 15f
   f. 18h + 13h
   g. 55m + 11
   h. 7 + 56y
2. Evaluate each of the expressions below.
   a. 6x + 21y and 3(2x + 7y) , x = 3 and y =4
   b. 5g + 7g and g(5 + 7), g = 6

Lesson Summary
An Expression in Factored Form: An expression that is a product of two or more expressions is said to be in factored form.

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Example 3

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Problem Set

1. Use models to prove that 3(a+b) is equivalent to 3a+3b.
2. Use greatest common factor and the distributive property to write equivalent expressions for the following expressions.
   a. 4d + 12e
   b. 18x + 30y
   c. 21a + 28y
   d. 24f + 56g

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