# a binomial thm problem

• January 10th 2008, 09:09 PM
afeasfaerw23231233
a binomial thm problem
a binomial thm problem
• January 10th 2008, 09:26 PM
Jhevon
Quote:

Originally Posted by afeasfaerw23231233
a binomial thm problem

i'm sorry. i don't see a much nicer way to do this problem. i would have done it with brute force like you did
• January 10th 2008, 10:28 PM
topsquark
$(1 + 2x)^4(1- x)^3$

The most clever thing I can come up with is to define two new variables:
$y = 1 + \frac{x}{2}$
and
$z = \frac{3x}{2}$

Then
$y + z = 1 + 2x$
and
$y - z = 1 - x$

Thus
$(1 + 2x)^4(1- x)^3 = (y + z)^4(y - z)^3$

$= [(y + z)^3(y - z)^3](y + z)$

$= (y^2 - z^2)^3(y + z)$

$= ([1 + 2x]^2 - [1 - x]^2)^3(1 + 2x)$
etc.

But I doubt this actually cuts down on the work load.

-Dan