Expanding Binomials

**BlueStar** · July 19th 2007, 11:26 AM

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).

**red_dog** · July 19th 2007, 11:35 AM

Do you mean $(r+4)^3$ ?

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

**Soroban** · July 19th 2007, 04:08 PM

Hello, BlueStar!

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

The very least you could do is mutliply it out . . .

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

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

The multiply by another $(r+4)$

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

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.

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