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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.

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2 x 3
2(x + 3)

Distributive property - used to multiply a single term and two or more terms inside a set of parentheses.

slide2

Distributive Property

Recall the distributive property of multiplication over addition . . .

symbolically:

a × (b + c) = a × b + a × c

distributive property
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
Example

2 (3x + 4)

2 (3x + 4)

6x +8

Rainbow Arrows!

practice
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
Variables Multiplied by Variables

Remember w * w = w2 - Not 2w!

Distribute

X(x + 3) x(y – 6)

X2 + 3xxy – 6x

distributing a negative
Distributing a Negative

-2(3x – 4)

-2(3x – 4)

-6x + 8

What is a negative times a positive?

Negative times a negative?

stop for today
Stop for today

Coming up!

Combining Like Terms!

Yea!

like terms
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
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

practice1
Practice

-2x2 + 7x

2x2 + 3x– 4x2 + 4x =

3xy + 2x + 3xy– 6x2– 2x2 =

-8x2 + 6xy + 2x

distributive property and combining like terms
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
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

practice2
Practice!

4x -2(x + 6)

4x – 2x – 12

2x -12  Final answer

22x + 3(x – 9)

22x + 3x – 27

25x -27  Final answer

challenge
Challenge

4y + 4(y-7) + 2(x+3)

4y + 4y – 28 + 2x + 6

8y – 28 + 2x + 6

8y - 22 + 2x  final answer