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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
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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 • 7 • 4 + 7 • 5 = 28 + 35 = 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