DON'T MIX UP [beautiful math coming... please be patient] $\,3x\,$ VERSUS [beautiful math coming... please be patient] $\,x^3\,$!

Some people confuse the shorthands for repeated addition and repeated multiplication.
The purpose of this section is to give you plenty of practice, so you won't confuse the two!

Exponents give a shorthand for repeated multiplication.
For example, [beautiful math coming... please be patient] $\,(\text{blah})^3 = \text{blah}\cdot\text{blah}\cdot\text{blah}\,$.
That is, [beautiful math coming... please be patient] $\,(\text{blah})^3\,$ represents three factors of blah.
Here are some examples:

[beautiful math coming... please be patient] $x^3 = x\cdot x\cdot x$
[beautiful math coming... please be patient] $(2x)^3 = (2x)(2x)(2x) = 8x^3$   You get the same result using an exponent law: $\,(2x)^3 = 2^3x^3 = 8x^3\,$
[beautiful math coming... please be patient] $(x+2)^3 = (x+2)(x+2)(x+2)$
Multiplication by an integer gives a shorthand for repeated addition.
For example, [beautiful math coming... please be patient] $\,3(\text{blah}) = \text{blah} + \text{blah} +\text{blah}\,$.
Here are some examples:

[beautiful math coming... please be patient] $3x = x + x + x$
[beautiful math coming... please be patient] $3(x+1) = (x+1) + (x+1) + (x+1) = 3x + 3$   You get the same result using the distributive law: $\,3(x+1) = 3x + 3$
[beautiful math coming... please be patient] $3(2x) = 2x + 2x + 2x = 6x$   You get the same result using the associative law: $\,3(2x) = (3\cdot 2)x = 6x$
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Equal or Opposites?
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
1 2 3 4 5 6
AVAILABLE MASTERED IN PROGRESS

What is this a shorthand for?