It can be summarized as follows: (1) Using formula method: We know that algebraic multiplication and factorization are inverse deformation. 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 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. Get the product form of factors, and then subtract the common factor of numerator and denominator. If the polynomial in the numerator or denominator can't decompose the factor, some items in the numerator and denominator can't be reduced separately. 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) 2, (. It can be changed into the sign of the whole fraction according to the sign law of the fraction, and then it can be treated as that the even power of-1 is positive and the odd power is negative. Of course, the numerator and denominator of a simple fraction can be multiplied directly. 6. Note that in the mixed operation, the brackets must be calculated first, then the power, then the multiplication and division, and finally the addition and subtraction of fractions. (8) Addition and subtraction of scores 1. General score. 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. Extended data:

The addition operation of rational number in conceptual formula is the same as the addition of two numbers with the same sign, and the absolute value is added with the same sign. Different symbols increase or decrease, large numbers determine and symbols. Add up the opposites of each other, and the result is that zero must be remembered well. Note that "big" minus "small" refers to the absolute value. The subtraction of rational numbers is equal to adding negative numbers, and the burden reduction is equal to adding positive numbers. The sign rule of rational number multiplication is that the sign of the same number is negative and a product is zero. Merging similar items When it comes to merging similar items, we must not forget the rules. Only the algebraic sum of the coefficients is found, and the letter index remains unchanged. Rules for deleting and adding brackets The key to deleting or adding brackets depends on the connection number. The expansion symbol is preceded by a plus sign, and the bracket invariant symbol is added. Parentheses are preceded by a minus sign, and when you add parentheses, they change sign. The solution equation is known and unknown, which leads to separation, which needs to be completed by moving. Shift addition, subtraction, addition, multiplication, division and multiplication. The sum of two numbers multiplied by the difference of two numbers is equal to the square difference of two numbers. Product and difference are two terms, and complete square is not it. The sum or difference square of two numbers in the complete square formula and its expansion * * *. The first and last square, the first and last two in the middle. The squares of sum are added and connected, and the squares of difference are subtracted and added. A complete square formula has the first square and the last square, and the second square has the first and the last square in the center. The squares of sum are added and then added, and the squares of difference are subtracted and then added. To solve a linear equation, first remove the denominator and then the brackets, and remember the sign change of the shift term. The coefficient "1" is not enough for the merger of similar items. To obtain the unknown quantity, the value must be checked and replaced. To solve a linear equation with one variable, first remove the denominator, then remove the brackets, then shift the terms and merge the similar terms. The coefficient of 1 is not ready yet, and the calculation is not in vain. References: