2(x + 3) Distributive property - used to multiply a single term and two or more terms inside a set of parentheses.

Distributive Property Recall the distributive property of multiplication over addition... symbolically: a × (b + c) = a × b + a × c

Distributive Property For any numbers a, b & c, it is true that a(b + c) = ab + ac Example: If we do the parenthesis first (PEMDAS) 2(2 + 5) = 2(7) = 14 or 2(2 + 5) = 2(2) + 2(5) = 14

Example 2 (3x + 4) 6x +8 Rainbow Arrows!

Practice 6(2 quarters + 3 nickels) = 12 quarters + 18 nickels = $3.90 5(3a + 2b) 15a + 10b 2(3n – 4) 6n - 8

Variables Multiplied by Variables Remember w * w = w 2 - Not 2w! Distribute X(x + 3)x(y – 6) X2 X2 + 3xxy – 6x

Distributing a Negative -2(3x – 4) -6x + 8 What is a negative times a positive? Negative times a negative?

Stop for today Coming up! Combining Like Terms! Yea!

Like Terms Terms that have the EXACT same variables or no variables. Example: 2x x -3x Like terms. 2x 4x 2 3xy2NOT like terms. Why?

Combining Like Terms If there are Like Terms, you can (and should) combine them to make a simpler expression. Example: 3x – x + 6x = 8x Try one 7b – 2b + 3b = 8b

Practice 2x 2 + 3x – 4x 2 + 4x = -8x 2 + 6xy + 2x -2x 2 + 7x 3xy + 2x + 3xy – 6x 2 – 2x 2 =

Distributive Property and Combining Like Terms 4(x-4) + 2x – 6 4x x – 6  First, distribute the 4 6x – 16 – 6  then, combine the x 6x - 22  then combine the constants

Another Example 12x – 6(x + 3) -5x + 2  what to distribute? 12x – 6x x + 2  combine like terms 12x – 6x x + 2 1x  combine constants 1x -16 or x -16  final answer

Practice! 4x -2(x + 6) 4x – 2x – 12 2x -12  Final answer 22x + 3(x – 9) 22x + 3x – 27 25x -27  Final answer

Challenge 4y + 4(y-7) + 2(x+3) 4y + – x + 6 8y – x + 6 8y x  final answer