3.8 The Distributive Property

Shows how multiplication affects addition or

subtraction

Example 1• 3 (5 + 7)• 3 (12)• 36• 3 (5 + 7)• 3 x 5 + 3 x 7• 15 + 21• 36

Distributive Property• Thinking of groups…• 3( x + 5) “Three times the quantity of

x plus 5”• The 3 tells us we have 3 groups that

each have an x and a five in them.• x 5 x 5 x 5• Added all together gives 3x + 15

Thinking of a Las Vegas card dealer…• 3 ( x + 5) 3 is the “dealer”

• 3 (x + 5) First, deal the 3 out to the x or just 3x• 3 (x + 5) Now, deal the 3 out to the 5 or 15

• Equals: 3x + 15

x3

53

3x + 15 is an expression that can not be simplified or

solved because • We don’t know the value of x• The two terms are unlike: 3x is an “x-term”

15 is a “non-x-term” (also called a “constant”)

Example 2

• Simplify 4 x 29• I can think of 29 as 30 -1• 4 ( 30 – 1)• 120 – 4• 116