Distribution & Combining Like Terms Review

Distribution & Combining Like Terms Review

Distributive Property

If I buy a bag of candy and give the whole bag to one person in the class, that wouldn't be fair! You would want me to distribute it evenly to everyone in the room. That's what the distributive property does. It takes a number and distributes it evenly to everyone in the group, or in our case, in the parentheses. We do this with multiplication.

Let's look at an example

The 5 is outside the parentheses. It needs to be distributed to everything INSIDE the parentheses by multiplying. 5 time x is 5x and 5 times 6 is 30. Therefore, we get

5x + 30!

Multiple Choice

Let's try one! Distribute & simplify 6(x + 3)

• 6x + 3

• 6x + 18

• 6x + 9

Sometimes there's extra stuff...

Only distribute to the stuff IN parentheses. If there's extra stuff in front of or after the parentheses, it doesn't get distributed. Just the stuff IN the parentheses.

Multiple Choice

Distribute 7x + 4(x -9)

• 7x + 4x - 9

• 28x + 4x - 36

• 7x + 4x - 36

• 13x + 4x - 5

Multiple Choice

Distribute -3(2x - 4) - 10 (be careful with your negatives!!)

• -6x - 12 - 10

• 6x - 12 - 10

• -6x + 12 - 10

• -6x + 12 + 30

Multiple Choice

Distribute 62 - 3(5x - 4)

• 62 - 15x + 12

• 62 + 15x + 12

• 62 - 15x - 4

• 62 + 15x - 4

But those problems weren't all the way simplified...

Yes! You are correct! AFTER you distribute, you then want to combine all the x's together and all the plain numbers together to get the BEST answer.

Multiple Choice

Going back to a problem we started earlier, combine like terms for

7x + 4x - 36

• 28x - 36

• -25x

• 11x - 36

Multiple Choice

Combine like terms 62 - 15x + 12

• -15x + 50

• -15x + 74

• 47x + 12

Multiple Choice

Distribute and combine like terms (aka fully simplify)

3(3x - 10) + 2x + 40

• 9x + 30

• 11x + 30

• 11x + 10

• 9x + 10

Multiple Choice

Simplify fully 12 + 2(x + 6)

• 12 + 8x

• 14x + 12

• 2x + 24

Multiple Choice

Combine like terms! (something crazy happens here and it's totally okay!)

9 - 4x + 4x - 5

• 14

• 4

• 5x - 5

• 9x - 5

Open Ended

Last one! You'll enter the answer to this one on your own. You don't need any special math characters in order to type this one in.

Simplify fully 8 - 2(2x + 1) + 5x