First, the principle:
The basic principle of splitting elimination is to make the difference between two algebraic expressions equal by adding or subtracting a rational number. This rational number is usually called "difference term", which can make some terms in algebraic expressions cancel each other out, thus simplifying the problem. The core idea of split term elimination method is to reduce the complexity of the original problem by using the difference term in algebraic expression and make it easier to solve.
Second, skills:
Identify the difference term: in the elimination of the split term, we need to identify the difference term in the algebraic expression first. The difference term is usually the difference between two algebraic expressions, which can be found by observing or analyzing the structure of algebraic expressions.
Clever addition and subtraction of difference term: once the difference term is determined, you can skillfully choose to add and subtract this difference term, so that the difference between two algebras becomes zero, thus eliminating the complexity of the original problem. When choosing addition and subtraction terms, we usually need to consider the overall structure of the problem and choose the most suitable operation.
Pay attention to symbols: when canceling the split items, pay special attention to the symbols of each item to ensure that the addition and subtraction of the difference items will not introduce wrong symbols and lead to incorrect results.
Organizational algebra: It is very important to organize algebra skillfully in the method of splitting elimination. By combining similar terms, distribution law, factorization and other mathematical skills, the algebraic structure can be clearer and easier to handle.
Flexible application: the split-term elimination method is not a universal method for all problems, and it needs to be applied flexibly according to the specific situation. When solving algebraic problems, we can try to use the split term elimination method to see if we can simplify the problem and improve the efficiency of solving problems.