# Expanding Binomials

• Jul 19th 2007, 11:26 AM
BlueStar
Expanding 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 AM
red_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 PM
Soroban
Hello, BlueStar!

Quote:

Find the expansion of: .\$\displaystyle (r + 4)^3\$
The very least you could do is 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.