Addition and subtraction of algebraic expressions
1. Use letters to represent numbers (basic knowledge of algebra)
1. Algebraic expression: the expression of the number of connections, and the letters indicating this number with the operation symbol "+-×℉ ..." are called algebraic expressions. Note: There are certain restrictions on using letters to represent numbers. First, the number obtained by letters should ensure that its formula is meaningful; second, the number obtained by letters should also make it meaningful in real life or production; A single number or letter is also algebraic; Formulas formed by connecting numbers and letters with basic operation symbols are called algebraic expressions, such as n,-1, 2n+500, abc.
2. Algebra writing specification:
(1) Numbers are multiplied by letters, or letters are usually multiplied by ""or omitted;
(2) When the numbers are multiplied, they should still be multiplied by "×", but not by "×", and the multiplication sign cannot be omitted;
(3) When a number is multiplied by a letter, the number is usually written in front of the letter in the result. For example, a×5 should be written as 5a;
(4) When the band fraction is multiplied by letters, the band fraction should be changed to a false fraction, for example, a× should be written as a;
(5) When there is a division operation in the algebraic expression, the division method and the division method are generally connected by a fractional line, such as the form written in 3 A;
(6) The difference between A and B should be written in alphabetical order; If we only talk about the difference between two numbers, when we set two numbers as A and B respectively, we should classify them and write them as a-b and B-A. 。
When there is division, it is expressed by fraction;
(7) If the operation result is an addition and subtraction formula, when there are units behind it, the whole formula should be enclosed in brackets.
3. Several important algebraic expressions: (m and n represent integers)
(1) The square difference between A and B is: A2-B2; The square of the difference between a and b is: (a-b) 2;
(2) If a, b and c are positive integers, the two-digit integer is 10a+b and the three-digit integer is10a+10b+c;
(3) If both m and n are integers, the quotient m is divided by 5, and the remainder n is 5m+n; Even numbers can be 2n, and odd numbers can be 2n+1; Three consecutive integers can be: n- 1, n, n+1;
(4) If b>0, if positive number is: a2+b, negative number is: -a2-b, non-negative number can be: a2, and non-positive number can be: -a2.
Two. algebraic expression
1. monomial: The algebraic expression representing the product of numbers and letters is called monomial. A single number or letter is also algebraic.
2. Coefficient of single item: numerical factor in single item; The numerical factor that is not zero in a single item is called the numerical coefficient of a single item, which is called the single item coefficient for short.
3. The number of monomials: the sum of the indices of all the letters in the monomials.
Polynomial: The sum of several monomials is called polynomial. Each monomial is called a polynomial term, and the term without letters is called a constant term.
The degree of the highest degree term in a polynomial is called the degree of the polynomial. The degree of the constant term is 0.
Note: (If A, B, C, P and Q are constants) ax2+bx+c and x2+px+q are two common quadratic trinomials.
Algebraic expression: monomials and polynomials are collectively referred to as algebraic expressions, that is, any algebraic expression that does not contain division or division but does not contain letters is called algebraic expression. Algebraic expressions are classified as:
Note: It is not an algebraic expression whose denominator contains letters.
6. Power-up and power-down permutation of polynomials: arranging the terms of a polynomial according to the exponent of a letter from small to large (or from large to small) is called power-up permutation (or power-down permutation) of this letter. Note: The final result of polynomial calculation should generally be ascending power (or descending power arrangement).
Three. Addition and subtraction of algebraic expressions
1. Merge similar projects
2 Similar items: items with the same letters and the same letter index are called similar items.
Rule for merging similar items: When the coefficients of similar items are added, the result will be taken as the coefficient, and the letters and their indexes will remain unchanged.
Four steps to merge similar items: (1) Find similar items accurately; (2) additive commutative law is used to combine similar items after exchanging positions; (3) Using the rule, the coefficients of similar items are added, and the index of letters remains unchanged; (4) Write the merged results.
5 de-bracket
Rules for removing brackets:
(1) brackets are preceded by "+". Remove the brackets and the "+"in front of them, and the symbols of the items in brackets remain unchanged;
(2) There is a "-"sign before the brackets. Remove the brackets and the "-"sign in front of them, and change the symbol of each item in brackets.
Rules for adding brackets: When adding brackets, if there is a "+"sign in front of the brackets, all items in the brackets remain unchanged; If there is a "-"before the brackets, all items in the brackets should be changed.
7 Algebraic addition and subtraction: if there are brackets in algebraic addition and subtraction, remove them first and then merge similar items; The addition and subtraction of algebraic expressions is actually to combine similar terms of polynomials on the basis of removing brackets.
Algebraic expression plus or minus 8 steps: (1) List algebraic expressions; (2) remove the brackets; (3) Parentheses (4) Merge similar items.
The seventh grade mathematics first volume second chapter related article knowledge summary:
★ Induction of knowledge points in the first volume of junior high school mathematics.
★ Summary of the second chapter of the first volume of junior high school mathematics handwritten newspaper
★ Summary of mathematical knowledge points in the first volume of the first day of junior high school.
★ Key points of the first volume of junior high school mathematics.
★ Addition and subtraction of algebraic expressions in the second chapter of Grade One Mathematics.
★ Summary of knowledge points in the first volume of junior high school mathematics
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★ Summarize the knowledge points of seventh grade mathematics in junior high school.