Distributive Property

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Transcript Distributive Property

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)
Rainbow
Arrows!
2 (3x + 4)
6x +8
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 = w2 - Not 2w!
Distribute
X(x + 3)
x(y – 6)
X2 + 3x
xy – 6x
Distributing a Negative
-2(3x – 4)
-2(3x – 4)
-6x + 8
What is a negative
times a positive?
Negative times a
negative?
Like Terms
Terms that have the EXACT same variables or
no variables.
Example:
2x x -3x
2x
4x2 3xy 2
Like terms.
NOT 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
2x2 + 3x – 4x2 + 4x = -2x2 + 7x
3xy + 2x + 3xy – 6x2 – 2x2 =
-8x2 + 6xy + 2x
Distributive Property and Combining
Like Terms
4(x-4) + 2x – 6
4x -16 + 2x – 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 -18 -5x + 2  combine like
terms
12x – 6x -18 -5x + 2
1x -18 + 2
 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 + 4y – 28 + 2x + 6
8y – 28 + 2x + 6
8y - 22 + 2x  final answer