First of all, a brief introduction.
1. Merging similar items is to add the coefficients of similar items by multiplication and division, and the obtained results are taken as coefficients, and the letters and indexes remain unchanged, which is actually the reverse application of multiplication and division;
2. Merging rules: After merging similar items, the coefficients of the obtained items are the sum of the coefficients of similar items before merging, and the letters and their indexes remain unchanged. The letters are unchanged, and the coefficients are added and subtracted; The coefficients of similar items are added together, and the results are taken as coefficients, and the indexes of letters and letters remain unchanged.
Second, related knowledge
1. If two monomials contain the same letters and the index of each letter is the same, they are called 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 the law that the results obtained by adding the coefficients of similar items are taken as coefficients, and the indexes of letters remain unchanged.
3. Theoretical basis for the merger of similar items: In fact, the rules for the merger of similar items have their theoretical basis. It is based on the well-known multiplication and distribution law, a(b+c)=ab+ac.
Third, mathematics.
The three main mathematical definitions of 1. are called logicians, intuitionists and formalists, each of which reflects a different school of philosophy. Everyone has serious problems, no one generally accepts it, and no reconciliation seems feasible. Many mathematical objects, such as numbers, functions, geometry, etc., reflect the internal structure of continuous operation or the relationships defined therein.
2. Mathematically study the properties of these structures. For example, number theory studies how integers are represented under arithmetic operations. In addition, things with similar properties often occur in different structures, which makes it possible for a class of structures to describe their state through further abstraction and then axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures.
3. Therefore, we can learn abstract systems such as groups, rings and domains. These studies (structures defined by algebraic operations) can form the field of abstract algebra.