**What is the Distributive Property in Arithmetic and Algebra?**
Named the 'Distributive Property (sometimes referred to as the distributive law) because in essence, you are distributing something as you separate or break it into parts. The distributive property makes numbers easier to work with. In algebra when we use the distributive property, we're expanding (distributing).

**The Distributive Property in Arithmetic:**

The Distributive Property lets you multiply a sum by multiplying each addend separately and then add the products. The Distributive Property helps with mental math and should be taught to children as a method to multiply much quicker in their heads. Children need lots of experience using the Distributive Property. Children make greater 'connections' with the ability to use the distributive propertly for mental math. For instance:

Let's say I have to quickly multiply:

4 x 53

(4 x 50) + (4 x 3)

200 + 12

212

In my mind, I can compute the answer of 4x50 quickly (200) then I add (4x3) 12 to give me 212. That's why using the Distributive property can come in handy!

Let's try another:

12x19 - Well 12 x 20 is easy, it's 240 But, I added one more 12 than I needed, so I'll take it away from 240 to give me 228.

One more!

4 x 27

=4(20 +7)

=4(20) + (7)

=80 + 28

=108

Students should have lots of opportunity to break numbers apart using the distributive property which greatly assists the mental math process.

**The Distributive Property in ALgebra:**

The Distributive Property is handy to help you get rid of parentheses.

a(b + c) = ab + ac

To multiply in algebra, you'll use the distributive law:

3x(x+4)

= 3x(x) + 3x(4)

=3x^{2}+12x

You can use the distributive Property to multiply a polynomial by a monomial. You will expand the product of the monomial and polynomial. You can use the distributive property to divide a polynomial by a monomial. Each term is divided by the monomial. You can also use the distributive property to find the product of binomials - as shown:

(x + y)(x + 2y)

=(x + y)x + (x + y)(2y)

=x^{2}+xy +2xy 2y^{2}

=x^{2} + 3xy +2y^{2}

Let's try one more:

2y(y-3)-3y(y+2)

=2y^{2}-6y-3y^{2}-6y

=-y^{2}-12y