# Easy factoring problem

## Main Question or Discussion Point

how to factor (x+3)^3

maybe foil after factoring?

thanks for any help.

CRGreathouse
Homework Helper

hmm, maybe i used the wrong terminolgy, i want to take it apart, is that possible?

is (x+3)^3 the same as (x+3)(x+3)^2

Hurkyl
Staff Emeritus
Gold Member
Ah, you want to expand it. (There are other synonyms too)

Yes, those two are the same; that's essentially the definition of raising something to the third power.

x^2 + 4x + 3

and end up with

(x+3)(x+1).

Last edited:
okay so to fully expand (x+3)^3

could i just take the foil of (x+3)^2 and then multiply by (x+3) again?

if so, i'm unsure how to multiply the x+3 and the foiled polynomial

(a+b)^2 = a^2 + 2ab + b^2
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

There's a really easy trick to finding these. Expanding expressions of the form (x+y)^n can be done as follows:

First write x^n. The coefficient of the next term is equal to the current coefficient multiplied by the current exponent of x, and divided by the term number. For the coefficient of the second term, this is 1 * n / 1 = n. Decrease the exponent of x by 1, and increase the exponent of y by 1. Repeat this process until you get to y^n.

If they are of the form (x-y)^n, the signs just alternate. If you're unsure, use the property that a - b = a + (-b).

Hope that helps!

HallsofIvy