Suppose we have the follwing two identities:
(Ax-26)(Bx^2+Cx+D)=8x^3-2197
and (Ex-52)(Fx^2+Gx+H)=8x^3-2197;

Compute the quantity ((13B/2 + 2D/13 + AB)+(13F/2+2H/13+EF)).

There's no need to expand and compare coefficients. The problem title already tells you that it's a difference of cubes. So the easiest thing to do is to factor and compare coefficients.

8x^3-2197=(2x-13)(4x^2+26x+169)
     =(4x-26)(2x^2+13x+84.5)
     =(8x-52)(x^2+6.5x+42.25)

We can easily see what the coefficients are equal to.

A=4
B=2
C=13
D=84.5
E=8
F=1
G=6.5
H=42.25

(13B/2 + 2D/13 + AB)+(13F/2+2H/13+EF)=55

Posted by np_rt on 2005-02-12 18:20:57