1, common factor extraction method

Definition: put forward the same common factor of each term and transform the original polynomial into the form of product. This deformation is called the common factor extraction method. Formula: a 2-b 2 = (a+b) (a-b).

2. Formula method

Definition: Use the square difference formula A 2-b 2 = (a+b) (a-b) or complete square sum formula (a+b) 2 = A 2+2ab+b 2 or complete square difference formula (a-b) 2 = A 2-2ab+b 2 to pair polynomials.

3. Double cross multiplication

Definition: When the decomposed formula is four terms, the binary multiplication should be considered for decomposition. Formula: ax 2+bx+c = (ax+c) (bx+a).

Application of factorization formula method

1, approximate score

The main purpose of simplification is to transform complex expressions or polynomials into simpler forms for easy understanding and calculation. Through factorization, a polynomial expression can be decomposed into the product of several algebraic expressions, which makes the expression easier to operate and simplify.

For example, a complex fraction can be transformed into the product of several simple fractions through factorization, which is easier to operate and simplifies the fraction.

2. Solve the equation

Factorization has an important application in solving equations. The solutions of many equations can be obtained by factorization. For example, a quadratic equation can be transformed into the product of two linear equations by factorization, so that the root of the equation can be found more easily.

Specifically, if a quadratic equation can be factorized into the form of (ax+b)(cx+d)=0, then the root of the equation is x=-b/a or X =-D/C.

Step 3 simplify the expression

Factorization can simplify expressions. Sometimes, a complex mathematical expression can be transformed into a simpler form by factorization, which makes it easier to understand and calculate. For example, for a long polynomial expression, it can be transformed into the product of several simpler polynomials by factorization, which makes it easier to find the coefficient and degree of each term.