 What are the different properties that can help simplify expressions?  Commutative Property  Commutative  Associative  Distributive These only work with addition and multiplication  Numbers/variables can be moved around in any order.  =  9y(5) = 5(9y)  8r 2 t = 8tr 2

 Associative Property  Distributive Property  Numbers can be grouped differently.  (5+7x)+6x = 5+(7x+6x)  3w(w) = 3(w*w)  Remove parentheses by multiplying everything on the inside by the outside term.

 Examples Watch negative signs  5(4x+2)  -3(4+5y)  2x(3x-8)  -8y(3y-2)

 How do you simplify expressions?  Distribute first to get rid of any parentheses. Combine like terms by adding or subtracting. When adding/subtracting, you can only combine like terms. If they do not have the exact same variable, they cannot be combined. Just add/subtract numbers in front, variable stays the same. When multiplying, any variable can be multiplied. Multiply the coefficients, add exponents on variables.

 Examples  2y+4x+8y  6x+2(2x+7)  4a 3 + 6a+3a 3 +8a  4(3n+9)+5n

 Examples  (a+2b)3-3a  5(m-7)-3m  4(2x-1)+10(x-5)  10-2(4x-3)

 How do you multiply binomials?  What is the FOIL method?  Two methods: FOIL, Magic Box  Order to multiply terms: First, Outer, Inner, Last  Think of as double distributing.

 Examples using FOIL  (x+3)(x+8)  (2x+8)(4x+3)  (3y-3)(2y+9)  (7w-4)(w-6)

 How do you multiply using the magic box?  (x+5)(2x+3)  Make a box using terms that are being multiplied. x5+ 2x + 3

 Examples using Magic Box  (x-5)(x+7)  (2y+3)(6y-7)  (4a-5)(3a+2)  (7y-4)(5y-1)