# Math Help - a binomial thm problem

1. ## a binomial thm problem

a binomial thm problem

2. 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

3. $(1 + 2x)^4(1- x)^3$

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