Matching method is a technique of directional deformation of mathematical formula (matching into a "complete square"), and the relationship between known and unknown is found through the formula, thus simplifying the complex. When making a formula, it is necessary to make appropriate predictions and use the skills of "dividing", "adding", "matching" and "gathering" reasonably, so as to complete the formula. Sometimes called "matching method".

The most common formula is identical deformation, so that the mathematical formula appears completely square. It is mainly suitable for the discussion and solution of known or unknown quadratic equations, quadratic inequalities, quadratic functions and quadratic algebra, or the translation transformation of quadratic curves without xy terms.

The most basic formula used in the matching method is the binomial complete square formula (A+B) = A+2AB+B, and various basic formula forms can be obtained by using this formula flexibly, such as:

a+b =(a+b)-2ab =(a-b)+2ab；

a+a b+b =(a+b)-ab =(a-b)+3ab =(a+)+(b)；

a+b+c+a b+ BC+ca =[(a+b)+(b+c)+(c+a)]

a+b+c =(a+b+c)-2(a b+BC+ca)=(a+b-c)-2(a b-BC-ca)=…

Combined with other mathematical knowledge and properties, there are some other formula forms, such as:

1+sin 2α= 1+2 sinαcosα=(sinα+cosα)；

x+=(x+)-2 =(x-)+2； ..... and so on.