In the expansion of (ax + by)8, the first three terms are 256x8, 6144x7y, and 64 512x6y2. Find the value(s) of numerical coefficients a and b. Is there more than one possible answer based on these conditions? Explain.

Answer 1

(ax + by)^8
first term is a^8 x^8 = 256 x^8
so
a^8 =256
256^(1/8) = 2
so a = 2
next term
8a^7x^7 by = 2^7 x^7 b y
8* 2^7 b = 6144
1024 b = 6144
b = 6
third term for fun
(8*7/2) (ax)^6 (by)^2
28 * 64 * 36 x^6 y^2
= 64,512 x^6y ^2 good, it worked.