1, square difference formula: a? -B? =(a+b)(a-b)

Among the formulas of trigonometric functions, there is a group of formulas called trigonometric square difference formula. Named after the square difference formula, it is mainly used to solve triangles.

2. Complete square formula: a? +2ab+b？ =(a+b)？

The square of the sum (or difference) of two numbers is equal to the sum of their squares, and the product of two numbers is added (or subtracted) twice to get a complete square formula.

The structural characteristics of this formula are: the product of two identical binomials on the left, and the trinomial on the right, which is the sum of the squares of the two terms on the left, plus or MINUS twice the product of these two terms (when the two terms are added); The letters in the formula can represent specific numbers (positive or negative numbers), and can also represent algebraic expressions such as monomials or polynomials.

3. Cubic sum formula: A? +b？ =(a+b)(a？ -ab+b？ )

Cubic sum formulas are sometimes used in mathematical operations. The literal expression of this formula is: the sum of two numbers, multiplied by the difference between their square sum and product, is equal to the cubic sum of these two numbers;

4. Cubic difference formula: a? -B? =(a-b)(a？ +ab+b？ )

Cubic difference formula is also one of the commonly used formulas in mathematics, which is in contact with high school mathematics and occupies a very important position in mathematical research, even in advanced mathematics and calculus. Cubic difference formula and cubic sum formula * * * are called complete cubic formula.

Five methods of factorization

First, the common factor method

If every term of a polynomial contains a common factor, then this common factor can be put forward, so that the polynomial can be transformed into the product of two factors. This factorization is called factorization.

Second, cross multiplication.

The specific method of cross multiplication: the multiplication on the left side of the cross is equal to the quadratic term coefficient, the cross multiplication is equal to the linear term coefficient, and the multiplication on the right side is equal to the constant term. Cross multiplication is the most important factorization method except common factor method and formula method, which is very convenient and widely used.

Third, the matching method

Generally, the items containing letters are first matched into a complete square form, leaving constant items, and then factorized by the square difference formula.

Fourth, the demolition method

According to the absolute value of the remaining project coefficient, the project to be dismantled is split.

Verb (abbreviation of verb) substitution method

The general law of factorization of substitution method: replace the same part in the original formula with a letter, then decompose the factor, and finally replace the letter, which is what you want.