(1) Using the formula method: We know that multiplication and factorization of algebraic expressions are inverse deformations. If the multiplication formula is reversed, the polynomial is decomposed into factors. So: A2-B2 = (a+b) (a-b) A2+2ab+B2 = (a+b) 2a2-2ab+B2 = (a-b) 2 If the multiplication formula is reversed, it can be used to decompose some polynomials. This factorization method is called formula method. (2) Square difference formula 1. Square difference formula (1) Formula: a2-b2=(a+b)(a-b) (2) Language: The square difference between two numbers is equal to the product of the sum of these two numbers and the difference between these two numbers. This formula is the square difference formula. (3) Factorization 1. In factorization, if there is a common factor, the common factor is first extracted and then further decomposed. 2. Factorization must be carried out until each polynomial factor can no longer be decomposed. (IV) Complete Square Formula (1) Reverse the multiplication formula (a+b)2=a2+2ab+b2 and (a-b)2=a2-2ab+b2, and you can get: a2+2ab+b2 = (A+B) 2a2-2ab+b2 = The above two formulas are called complete square formulas. (2) Form and characteristics of completely flat mode ① Number of terms: three terms 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 We 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 then decompose the factor by formula method. If we divide it into two groups (am+ an) and (bm+ bn), these two groups can separate the factors by extracting common factors. The original formula = (AM+AN)+(BM+BN) = A (m+n)+B (M+N). This step is not called polynomial factorization, 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 we can continue. (a+b)。 This method of decomposing factors by grouping is called grouping decomposition method. As can be seen from the above example, if all the items 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 the group decomposition method. (6) The extraction method of common factor is 1. When decomposing polynomial factors by extracting common factors, first observe the structure of polynomials. Determine the common factor of polynomial. When the common factor of polynomial is polynomial, it can be transformed into monomial by setting auxiliary elements, or the common factor can be extracted directly by taking this polynomial factor as a whole. When the common factor of the polynomial term is implicit, the polynomial should be deformed or changed in sign appropriately until the common factor of the polynomial can be determined. 2. When factorizing with the formula x2 +(p+q)x+pq=(x+q)(x+p), we should pay attention to: 1. A constant term must first be decomposed into the product of two factors. (2) Try to find which two factors are equal to the first-order coefficient. (3) Decompose the original polynomial into the form of (x+q)(x+p). (7) Multiplication and division of fractions. (1) Reducing the common factor of the numerator and denominator of a fraction is called a fraction of a fraction. (2) The purpose of score reduction is to simplify this score. First, we can consider decomposing into factors to get the product form of factors, and then we can omit the common factor of numerator denominator. If the polynomial in the numerator or denominator can't decompose the factor, we can't separate some items in the numerator and denominator at this time. 4. Pay attention to the correct use of the sign law of power in fractional reduction, such as x-y =-(y-x), (x-y) 2 = (y. (x-y) 3 =-(y-x) 3.5. The numerator or denominator of a fraction with a signed power n can be changed into the sign of the whole fraction according to the law of fractional sign, and then the even power of-1 is regarded as positive and the odd power as negative. Of course, the numerator and denominator of a simple fraction can be directly multiplied. 6. First of all, pay attention to the mixing operation. Finally, add and subtract. (8) Addition and subtraction of scores 1. Although both general fractions and reduced fractions are for fractions, they are two opposite variants. Reduced scores are for one score, and general scores are for multiple scores; Simplification is to simplify fractions, and general fractions are to simplify fractions, thus unifying the denominator of each fraction. 2. The general score and reduction are deformed according to the basic properties of the score, and their similarity is to keep the value of the score unchanged. 3. Generally, in the general fractional results, the denominator is written as an unexpanded continuous product, and the molecular multiplication is written as a polynomial. Prepare for further operation. 4. The basis of general score: the basic nature of score. 5. The key to general scores: determine the common denominator of several scores. Usually, the product of the highest power of all factors of each denominator is taken as the common denominator, and such common denominator is called the simplest common denominator. 6. Simulate the general fraction of a fraction to find the general fraction of a fraction: turn several fractions with different denominators into fractions with the same denominator equal to the original fraction, which is called addition and subtraction of fractions with the same denominator, and addition and subtraction of molecules, that is, the operation of fractions is transformed into the operation of algebraic expressions. 8. Addition and subtraction of fractions with different denominators: addition and subtraction of fractions with different denominators are divided into fractions with the same denominator first, and then added and subtracted. 9. Fractions with the same denominator are added and subtracted, and the denominator remains the same. It's just the addition and subtraction of molecules, but it should be noted that each molecule is a whole, and brackets should be added in due course. 10. For the addition and subtraction between algebra and fraction, algebra is regarded as a whole. To divide. 1 1. For addition and subtraction of fractions with different denominators, first observe whether each formula is the simplest fraction. You can simplify the fraction first and then divide it, which can simplify the operation. 12. As the final result, if it is a score, it should be the simplest score. (9) unary band letter coefficient. This number is represented by X. According to the meaning of the question, the equation ax=b(a≠0) can be obtained. In this equation, X is an unknown number, and A and B are known numbers in letters. For x, the letter a is the coefficient of x and b is a constant term. This equation is a one-dimensional linear equation with letter coefficients. The solution of the letter coefficient equation is the same as that of the numerical coefficient equation, but special attention should be paid to: multiply or divide two sides of the equation with a letter, and the value of this formula cannot be equal to zero.