Find the expansion of (r+ 4)</I>3

I have the hardest time ever with this topic. I need a good, clear explanation on how to expand these (for someone who's an apparent math moron).

Printable View

- Jul 19th 2007, 11:26 AMBlueStarExpanding Binomials
Find the expansion of (

*r*+ 4)</I>3

I have the hardest time ever with this topic. I need a good, clear explanation on how to expand these (for someone who's an apparent math moron). - Jul 19th 2007, 11:35 AMred_dog
Do you mean $\displaystyle (r+4)^3$ ?

$\displaystyle (a+b)^3=a^3+3a^2b+3ab^2+b^3$ - Jul 19th 2007, 04:08 PMSoroban
Hello, BlueStar!

Quote:

Find the expansion of: .$\displaystyle (r + 4)^3$

*mutliply it out . . .*

First, find $\displaystyle (r +4)^2$

. . $\displaystyle (r + 4)^2 \;=\;(r+4)^2 \;=\;r^2 + 4r +4r + 16 \;=\;r^2 + 8r + 16$

The multiply by another $\displaystyle (r+4)$

. . $\displaystyle (r+4)(r^2 + 8r + 16) \;=\;r^3 + 8r^2 + 16r + 4r^2 + 32r + 64 \;=\;\boxed{r^3 + 12r^2 + 48r + 64}$

If you are seeking a shortcut to this type of multiplication,

. . then you want the Binomial Theorem (or Binomial Expansion).

Perhaps someone will explain it to you . . . or not.