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Polygenic genetics help (IB)

A polygenic character is controlled by two genes each with two alleles. How many different possible genotypes are there for this character?
A. 2
B. 4
C. 9
D. 16

I chose B but the answer is C and my textbook isn't much help so does anyone know why?

Reply 1

purple-girl

AABB
AABb
AAbb
AaBB
AaBb
Aabb
aaBB
aaBb
aabb

so 9 different genotypes...although it only gives 4 different phenotypes (as AA and Aa give the same phenotype, as do BB and Bb cos they have the dominant allele).