Distributive Property and Factoring

Definition of Distributive Property Axiom  For any numbers, a, b, and c, a(b+c)=ab+ac  For any numbers, a, b, and c, (b+c)a=ba+bc

Distribution  The distributive property must be used to remove parentheses in an equation  7(4+5)=7(9)=63  = = 63

Distribution  Distributing a number is like taking a basket of red M & Ms and giving one to each student in the class

Definition of Factoring Axiom  If the statement of the distributive property is reversed, we have the basis of a process called factoring  ab + ac = a (b + c)

Factoring  Factoring is like taking all the red M & Ms from the students and putting them back into the basket

Factoring Examples 8x + 8 y = 8(x + y) 3x + 3y + 3z + 3(x + y + z)

Comprehension Questions  What is the difference between distributing a number and factoring a number in an expression or in an equation?  How do you know when to do what?  What picture should you have in your head when you try to figure this out?  What ideas do you have to help you remember?

Fun Facts  Distribution and Factoring are the building blocks of algebra!  They are the “buzz words” you need to learn in order to be successful