The parents are geno typically heterozygous in all genes. They all express the dominant trait, while their offspring is homozygous recessive. Homozygous dominant, and heterozygous, with some expressing the dominant traits, others the recessive traits. If the genes are unlinked, so that the traits are independent, you'd have 2^4 = 16 different combinations when experimenting with 4 genes. Thats why P1 is alike and all F1 is different. Those are the reasons.
http://wiki.answers.com/Q/Why_Mendel_perform_experiments_on_pea_plant
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