1, three forms of algebraic expression multiplication:

(1) Single item multiplied by single item;

(2) Polynomial multiplied by monomial: a(m+n)= am+an.

(3) Polynomial multiplied by polynomial: (a+b)(m+n)= am+an+bm+bn.

2. Multiplication formula:

Multiplication formula (1)

Second, factorization:

Decomposition of a polynomial into the product of several simplest algebraic expressions is called decomposition of this polynomial or decomposition.

(Note: The simplest algebraic expression is an algebraic expression that cannot be reduced to the product of several algebraic expressions. )

Three, factorization method:

1, increase the common factor: ma+mb+mc = m(a+b+c),

The coefficient of common factor is the greatest common divisor of polynomial coefficient;

Letters are the same letters contained in each term of a polynomial;

The index of the same letter takes the smallest term, that is, the lowest power.

2. Formula method:

a^2-b^2=(a+b)(a-b)； (square difference formula)

Complete square formula:

Complete square formula (2)

3. Cross multiplication:

x^2+ (p+q)x + pq =(x+p)(x+q)

For example: x 2+ 14x+45 = (x+5) (x+9).

Fourth, factorization steps:

1, first decompose by common factor method, then decompose by formula method, and then see if the decomposition can continue.

2. Finally, the decomposition result is expanded by algebraic expression multiplication, and compared with the original formula to test its correctness.

Five, factorization matters needing attention:

Factorization should be thorough, that is, the decomposition result should be in the form of the product of several simplest algebraic expressions!