The so-called formula is to make an analytical formula into the form of the sum of positive integer powers of one or more polynomials by using the method of constant deformation. The method of solving mathematical problems through formulas is called matching method, and the most commonly used method is completely flat method. Matching method is an important method of constant deformation in mathematics, which is widely used in factorization, simplifying roots, solving equations, proving equality and inequality, solving functions and so on.

2, factorization method

Factorization is to change a polynomial into the product of several algebraic expressions. Factorization is the basis of identity deformation. As a powerful mathematical tool and method, it plays an important role in solving algebra, geometry, trigonometry and other problems. There are many methods of factorization, except extracting common factors, formulas, grouping decomposition, cross multiplication and so on. Middle school textbooks also introduce adding items by splitting items and root decomposition.

3. Alternative methods

Method of substitution is a very important and widely used method to solve mathematical problems. We usually refer to unknowns or variables as elements. The so-called method of substitution is to replace a part of the original formula with new variables in a more complicated mathematical formula, so as to simplify it and make the problem easy to solve.

4. Discriminant method and Vieta theorem.

The root discrimination of unary quadratic equation ax2+bx+c=0(a, B, C belongs to R, a≠0) and△ = B2-4ac is not only used to judge the properties of roots, but also widely used in algebraic deformation, solving equations (groups), solving inequalities, studying functions and even geometric and trigonometric operations as a problem-solving method.

Vieta's theorem not only knows one root of a quadratic equation, but also finds another root. Knowing the sum and product of two numbers, we can find the symmetric function of the root, discuss the sign of the root of quadratic equation, solve the symmetric equation and solve some problems about quadratic curve. , has a very wide range of applications.