﻿ Don't Mix Up 3x versus x^3!
DON'T MIX UP $\,3x\,$ VERSUS $\,x^3\,$!

by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
• PRACTICE (online exercises and printable worksheets)

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, $\,(\text{blah})^3 = \text{blah}\cdot\text{blah}\cdot\text{blah}\,$.
That is, $\,(\text{blah})^3\,$ represents three factors of blah.
Here are some examples:

$x^3 = x\cdot x\cdot x$
$(2x)^3 = (2x)(2x)(2x) = 8x^3$   You get the same result using an exponent law: $\,(2x)^3 = 2^3x^3 = 8x^3\,$
$(x+2)^3 = (x+2)(x+2)(x+2)$

Multiplication by an integer gives a shorthand for repeated addition.
For example, $\,3(\text{blah}) = \text{blah} + \text{blah} +\text{blah}\,$.
Here are some examples:

$3x = x + x + x$
$3(x+1) = (x+1) + (x+1) + (x+1) = 3x + 3$   You get the same result using the distributive law: $\,3(x+1) = 3x + 3$
$3(2x) = 2x + 2x + 2x = 6x$   You get the same result using the associative law: $\,3(2x) = (3\cdot 2)x = 6x$
Master the ideas from this section