The best cross to find out if the purple-flowered peas are homozygous is a monohybrid cross. In a monohybrid cross, the scientist would cross the purple-flowered pea plant with another pea plant that has a different flower color (such as white), and observe the phenotype (observable characteristics) of the offspring.
If the purple-flowered pea plant is homozygous for the purple flower color (PP), all of the offspring will also have purple flowers. However, if the purple-flowered pea plant is heterozygous (Pp) for the purple flower color, some of the offspring will have white flowers. This is because the offspring will inherit one allele (version) of the gene for flower color from each parent. If the purple-flowered parent is homozygous, it will pass on a purple allele in each case; if it is heterozygous, it will pass on either a purple or white allele.
By observing the flower color of the offspring, the scientist can determine whether the parent plant is homozygous or heterozygous for the purple flower color allele. If all the offspring have purple flowers, the parent plant is homozygous. If some of the offspring have white flowers, the parent plant is heterozygous.