Distributive and Expanding Expressions

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Expanding & Factoring Expressions Word Problems

• Look for MULTIPLICATION problems

• AREA questions are popular

​Word Problems

• Expanding an expression happens when you use the distributive property

• Example: 5(2x + 8) becomes 10x + 40

​The Distributive Property

Expanding Expressions

Multiple Choice

Five friends went to Chipotle to eat lunch and they all got the same thing. Each meal cost "x" dollars plus $2 for the drink. Write an expression and expand it to show the cost of lunch for all five friends.

• 2(x + 5)

  2x + 10

• 5(2x)

  10x

• 5(x + 2)

  5x + 10

• 5 + x + 2

  x + 7

Multiple Choice

Each row in a classroom has 11 girls and "b" boys. There 9 rows in that class. Write a numerical expression and expand it to show the number of students in that class.

• 11(9 + b)

  99 + 11b

• 11(9b)

  99b

• 9(11b)

  99b

• 9(11 + b)

  99 + 9b

Multiple Choice

Mr. Boughton gave each of his three children a $20 bill and a check for their birthdays (all of which are in March). Which expression represents the total amount he gave?

• 100(c x 20)

  100c x 2000

• 3(c x 20)

  3c x 60

• 3(c + 20)

  3c + 60

• 20(c + 3)

  20c + 60

Multiple Select

CHOOSE TWO:

Find the TWO expressions that represent the area of the given rectangle:

• 10(3x - 1)

• 10 + 3x - 1

• 30x - 1

• 30x - 10

• Look for DIVISION problems

​Word Problems

• Factoring an expression happens when you find the greatest common factor and divide it.

• Example: 8x + 40 becomes 8(x + 5)

​REVERSE Distributive Property!!

Factoring Expressions

Multiple Choice

The area of a rectangle is given by the expression 9x - 108 square inches. Factor to find the possible side lengths of the rectangle.

• 9(x - 108)

• 9(x - 12)

• -99x

• 3(3x - 24)

Match

A group of students go to the movies. The cost of the movie and all of the snacks is given by the expression 7x + 42. Each student paid the same for the movie and had the same snack. Factor the expression to find out how many students went and what each person paid.

• 7(x + 6)

• 7

• (x + 6)

• $77

The factored expression

The number of people who went

The cost of the movie and snack together

The total cost if the movie was $5 each

• The factored expression

• The number of people who went

• The cost of the movie and snack together

• The total cost if the movie was $5 each