# Distributive Property(2)

```					               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)   What is a negative
times a positive?
-6x + 8     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   4x2 3xy 2     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
2           2                 2
2x + 3x – 4x + 4x = -2x + 7x

2   2
3xy + 2x + 3xy – 6x – 2x =
2
-8x + 6xy + 2x
Distributive Property and Combining
Like Terms
4(x-4) + 2x – 6
4x -16 + 2x – 6 àFirst, distribute
the 4
6x – 16 – 6     à then, combine the x
6x - 22         à then combine the
constants
Another Example
12x – 6(x + 3) -5x + 2 à what to
distribute?
12x – 6x -18 -5x + 2 à combine like
terms
12x – 6x -18 -5x + 2
1x -18 + 2          à combine constants

1x -16   or x -16 ß final answer
Practice!
4x -2(x + 6)
4x – 2x – 12

22x + 3(x – 9)
22x + 3x – 27
Challenge
4y + 4(y-7) + 2(x+3)
4y + 4y – 28 + 2x + 6
8y – 28 + 2x + 6
8y - 22 + 2x ß final answer

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Jun Wang Dr
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