Algebraic formula is the most basic formula in algebra, so it is necessary to introduce algebraic formula and learn the following contents (such as fractions, quadratic equations with one variable, etc.). ). On the basis of studying rational number operations, simple algebraic expressions, linear equations and inequalities, algebraic expressions are introduced. In fact, the relevant contents of algebraic expressions have been learned in the sixth grade, but now the contents of algebraic expressions are more applicable than in the past, which increases the background of practical application.

There are many knowledge points in this chapter that are important or difficult. The key points and difficulties are as follows.

First, the four operations of algebraic expressions

Addition and subtraction of 1. algebraic expressions

Merging similar items is the key and difficult point. When merging similar items, we should pay attention to the following three points: ① Only by mastering the concept of similar items can we distinguish similar items and accurately grasp the two standard letters and letter indexes for judging similar items; (2) The definition of merging similar terms means merging similar terms in polynomials into one term. After merging similar terms, the number of terms in the polynomial will decrease, thus simplifying the polynomial. (3) "Merging" refers to adding the coefficients of similar items, and the obtained results are used as new coefficients, and the letters and letter indexes of similar items should remain unchanged.

2. Multiplication and division of algebraic expressions

The emphasis is on multiplication and division of algebraic expressions, especially multiplication formulas. It is difficult for students to master the structural characteristics of multiplication formula and the broad meaning of letters in the formula. Therefore, the flexible application of multiplication formula is difficult, and the handling of symbols in brackets is another difficulty when adding (or removing) brackets. Parentheses (or brackets) are the deformation of polynomials, which should be carried out according to the law of parenthesis (or brackets). In the multiplication and division of algebraic expressions, the single multiplication and division is the key, because the multiplication and division of general polynomials should be "transformed" into the single multiplication and division.

The main problems of the four operations of algebraic expressions are:

Four operations of (1) monomial

This kind of questions mostly appear in the form of multiple-choice questions and application questions, which are characterized by examining four operations of a single item.

(2) Operation of monomial and polynomial

This kind of problems mostly appear in the form of solving problems, which are highly skilled and characterized by examining the four operations of monomials and polynomials.

(3) Polynomials and polynomial operations.

This kind of questions mostly appear in the form of fill-in-the-blank questions and solution questions, which are characterized by examining the four operations of polynomials and being skillful.

Second, factorization.

The difficulty lies in two basic methods of factorization. Factorization is the reverse deformation of algebraic expression multiplication, and the introduction of factorization should firmly grasp this point.

Third, make good use of the selected content.

"Reading and Thinking" and "Observation and Guess" are two optional columns in the textbook, and their contents are the expansion and extension of related knowledge. "Yang Hui Triangle" can not only help students understand the laws of various coefficients in some binomial expansions, improve their mathematical literacy, but also cultivate their patriotic feelings imperceptibly.

Classification and solution of numerical simplified evaluation problems

Algebra simplified evaluation is an important and difficult content in junior high school mathematics teaching. Students can't find the starting point when solving problems, and choosing the wrong method often gets twice the result with half the effort. How to improve learning efficiency and tide over difficulties smoothly, the author classifies and summarizes this problem and discusses its solutions for students' reference.

1. The given algebraic expression is simplified if the known conditions are not simplified.

2. Given the simplification of conditions, given algebra is not simplified.

3. Known conditions and given algebraic expressions should be simplified.