(a) using the formula method:

We know that algebraic multiplication and factorization are inverse deformations of each other. If the multiplication formula is reversed, the polynomial is decomposed into factors. So there are:

a2-b2=(a+b)(a-b)

a2+2ab+b2=(a+b)2

a2-2ab+b2=(a-b)2

If the multiplication formula is reversed, it can be used to factorize some polynomials. This factorization method is called formula method.

(2) Variance formula

1. Variance formula

Equation (1): a2-b2=(a+b)(a-b).

(2) Language: the square difference of two numbers is equal to the product of the sum of these two numbers and the difference of these two numbers. This formula is the square difference formula.

(3) Factorization

1. In factorization, if there is a common factor, first raise the common factor and then decompose it further.

2. Factorization must be carried out until each polynomial factor can no longer be decomposed.

(4) Complete square formula

(1) Reversing the multiplication formula (a+b)2=a2+2ab+b2 and (a-b)2=a2-2ab+b2, we can get:

a2+2ab+b2 =(a+b)2

a2-2ab+b2 =(a-b)2

That is to say, the sum of squares of two numbers, plus (or minus) twice the product of these two numbers, is equal to the square of the sum (or difference) of these two numbers.

Equations a2+2ab+b2 and a2-2ab+b2 are called completely flat modes.

The above two formulas are called complete square formulas.

(2) the form and characteristics of completely flat mode

① Number of projects: three projects.

② Two terms are the sum of squares of two numbers, and the signs of these two terms are the same.

A term is twice the product of these two numbers.

(3) When there is a common factor in the polynomial, the common factor should be put forward first, and then decomposed by the formula.

(4) A and B in the complete square formula can represent monomials or polynomials. Here as long as the polynomial as a whole.

(5) Factorization must be decomposed until every polynomial factor can no longer be decomposed.

(5) Grouping decomposition method

Let's look at the polynomial am+ an+ bm+ bn. These four terms have no common factor, so we can't use the method of extracting common factor, and we can't use the formula method to decompose the factors.

If we divide it into two groups (am+ an) and (bm+ bn), these two groups can decompose the factors by extracting the common factors respectively.

Original formula =(am +an)+(bm+ bn)

=a(m+ n)+b(m +n)

Doing this step is not called factorization polynomial, because it does not conform to the meaning of factorization. But it is not difficult to see that these two terms still have a common factor (m+n), so they can be decomposed continuously, so

Original formula =(am +an)+(bm+ bn)

=a(m+ n)+b(m+ n)

=(m +n)？ (a +b)

This method of decomposing factors by grouping is called grouping decomposition. As can be seen from the above example, if the terms of a polynomial are grouped and their other factors are exactly the same after extracting the common factor, then the polynomial can be decomposed by group decomposition.