2(x + 3)

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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)

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)

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 = w2 - Not 2w!

Distribute

X(x + 3) x(y – 6)

X2 + 3xxy – 6x

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

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

-2x2 + 7x

2x2 + 3x– 4x2 + 4x =

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

22x + 3(x – 9)

22x + 3x – 27