Distributive Property (7-1)

Distributive Property

By John Townsend

​When you have an expression like 10x – 15, you can't subtract the 15 from the 10x. Order of operations tell us to do the multiplication first (10 times x) and then subtract 15. But we don't know the value of x so we can't multiply by 10.

​

10x – 15 is in simplest form.

​Here are some more examples:

Multiple Choice

Simplify: $$5\left(2n-3\right)$$  

• $$10n+15$$  

• $$10n-15$$  

• $$7n-15$$  

• $$7n-3$$  

Multiple Choice

Simplify: $$8\left(5-2w\right)$$  

• $$40-2w$$  

• $$5-16w$$  

• $$40-16w$$  

•   $$85-2w$$  

Multiple Choice

Simplify: $$3\left(a+7\right)$$  

• $$10a$$  

• $$3a+7$$  

• $$24a$$  

• $$3a+21$$  

Multiple Select

Which expressions are equivalent to

$$15r+18$$  

• $$3\left(5r+6\right)$$  

• $$5\left(3r+6\right)$$  

• $$3\left(6+5r\right)$$  

• $$3\left(5r\right)+3\left(6\right)$$  

• $$15+18r$$