Let's determine which cross will produce only heterozygous offspring. We'll evaluate each option one by one, examining the types of offspring each cross will produce.
1. Cross [tex]\(Aa \times Aa\)[/tex]:
- Genotype combinations:
- [tex]\(AA\)[/tex] (homozygous dominant)
- [tex]\(Aa\)[/tex] (heterozygous)
- [tex]\(aA\)[/tex] (heterozygous, same as [tex]\(Aa\)[/tex])
- [tex]\(aa\)[/tex] (homozygous recessive)
- Offspring genotypes: 1 [tex]\(AA\)[/tex], 2 [tex]\(Aa\)[/tex], 1 [tex]\(aa\)[/tex]
- This cross produces both homozygous dominant, heterozygous, and homozygous recessive offspring, not just heterozygous.
2. Cross [tex]\(Aa \times aa\)[/tex]:
- Genotype combinations:
- [tex]\(Aa\)[/tex] (heterozygous)
- [tex]\(aa\)[/tex] (homozygous recessive)
- Offspring genotypes: 1 [tex]\(Aa\)[/tex], 1 [tex]\(aa\)[/tex]
- This cross produces both heterozygous and homozygous recessive offspring, not just heterozygous.
3. Cross [tex]\(AA \times Aa\)[/tex]:
- Genotype combinations:
- [tex]\(AA\)[/tex] (homozygous dominant)
- [tex]\(Aa\)[/tex] (heterozygous)
- Offspring genotypes: 1 [tex]\(AA\)[/tex], 1 [tex]\(Aa\)[/tex]
- This cross produces both homozygous dominant and heterozygous offspring, not just heterozygous.
4. Cross [tex]\(AA \times aa\)[/tex]:
- Genotype combinations:
- [tex]\(Aa\)[/tex] (heterozygous)
- Offspring genotypes: 1 [tex]\(Aa\)[/tex]
- This cross produces only heterozygous offspring.
After evaluating all the options, we can see that the cross [tex]\(AA \times aa\)[/tex] is the one that produces only heterozygous offspring.
Therefore, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
