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If two monomials contain the same letters and the index of each letter is the same, they are called similar terms. For example, 2ab and-3ab, m2n and nm2 are similar terms. In particular, all constant terms are similar terms.
Merging similar terms in polynomials into one term is called merging similar terms (or merging similar terms). The combination of similar items should follow this law: the coefficients of similar items are added, and the result is taken as the coefficient, and the index of letters remains unchanged.
Is there a theoretical basis for why we should add up the coefficients of similar items without changing the index of letters and letters?
In fact, the merger rule of similar items has its theoretical basis. It is based on the well-known multiplication and distribution law, A (B+C) = AB+AC. Merging similar terms is actually the reverse application of the law of multiplication and distribution. That is, every item in the same category is regarded as the product of two factors. Because each item contains the same letters and their indexes are the same, each item in the same category contains the same factor. When merging, the distribution law is applied in reverse, and the same factor is multiplied by the algebraic sum of another factor in each term.