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 x

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 5x 5x 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

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) 120 – 4 116