Given that the coefficient of x² in the expansion of
( 1 + px )^4 * ( 1 + qx )^3
is -6, and that
p + q = 1,
find the values of p and q.
The answers are:
p = 2, q = -1
or
p = -2, q = 3.
I know how to expand the equations... choose and everything. But apparently there's a less tedious way to find out the coefficient of x² with multiple expansions.
For a simpler one, such as (1+4x)(2-x)^6, I know that you get two terms with x²:
(1)......1*15(2^4)(-x)² = 240x²
(2)......4x*(6)(2^5)(-x) = -768x²
(1)+(2) = -528x²
And hence you get the coefficient of x².
But for (1+px)^4 * (1+qx)^3, it's obviously different because both expansions have powers and henceforth I'll have to multiply certain terms here and there to get the final coefficient of x² ... it's too complicated, though, if I'll have to expand everything. Is there a simpler way to do it, and could you provide a working? Thanks!
2007-06-08
18:51:41
·
4 answers
·
asked by
kimiessu
2