### distribute to expand, simplify, or factor

Intro

It is not necessary to distribute until variables are used in algebra.
On the left, arithmetic syntax of order of operations is used.
On the right, the algebraic techniques of the distributive property is used.
```arithmetic   algebra
2(4 + 5) = 2(4 + 5)
2(9)   = 2(4)+2(5)
18	 =  8 + 10
18 	 = 18```
The arithmetic use of inclusion marks or parentheses is easier.

You try it.

If you'd like,
1st: Mentally compute the value using order of operations.
2nd: Use the distributive property to simplify 3( 4 + 5 - 6 - 3)

So, Why Is The Distributive Property Needed?

The essay Most Operations Are Not Distributive gives examples
In short, you need it to expand and factor expressions which are
the sum or difference of variable and constant terms.
One use undoes the other.
 Distribute to expand: 3(x + 4) Answer 3(x + 4) 3(x) + 3(4) 3x + 12 Distribute to factor: 3x + 12 Answer 3x + 12 3(x) + 3(4) 3(x + 4)

The Distributive Property in Use

I. Simplify expressions 1 and 2 then check each answer.
1.] 3(x - 5) - 2(x + 3 - 2y)

2.] -52 - 4(x - y) + 40 - 04

II. Solve equations 3 which uses the expressions from problems 1 and 2.
3.] 3(x - 5) - 2(x + 3 - 2y) = -52 - 4(x - y) + 40 - 04

III. Simplify expressions 4 and 5 then check each answer.
The caret, ^ , is used to indicate exponentiation.
4.] 5x(x2 + 4x - 3) - (x3 - 4x2 - 4)

5.] 3(6 - 7)3 - 22(3 - ( 5 - 1))

IV. Solve equation 6 which uses the expressions from problems 4 and 5 and other terms.
6.] 5x(x2 + 4x - 3) - (x3 - 4x2 - 4) = {3(6 - 7)3 - 22(3 - ( 5 - 1)) } + 4x3 + 24x2