Add and subtract several integers, usually with parentheses, then remove the parentheses, and merge

Merging the same type means that each item contains the same letters, and the same number of times is the same.

If the parentheses are preceded by a plus sign, the parentheses can be removed directly, and the symbol remains unchanged.

If the parentheses are preceded by a negative sign, each item in the parentheses must be preceded by a negative sign on the basis of the original coefficient.

For example, -(a b+ab-ab 2)=-a b-ab+ab 2

Several integers are added and subtracted, usually in parentheses (enclosing each integer involved in the addition and subtraction operation), and then removing the parentheses to merge similar terms.

Several integers are added and subtracted, usually separated by parentheses, and then de-parentheses, merging similar terms.

Two: addition and subtraction of integers.

Knowledge Networks: Concepts, Definitions:

1. A formula that is the product of a number or a letter is called a monomial, and a single number or letter is also a monomial.

2. The numerical factor in the mononomial is called the coefficient of the monomial.

3. The sum of the exponents of all letters in a monomial is called the degree of a monomial.

4. The sum of several single terms is called a polynomial, where each mononomial is called a term of a polynomial, and an term without a letter is called a constant term

term）。

5. The number of terms with the highest number in a polynomial is called the degree of a polynomial.

6. Merging the same terms in the polynomial into one is called merging the same terms.

After merging the same kind of items, the coefficients of the obtained items are the sum of the coefficients of the same kind of terms before the merger, and the letter part remains unchanged.

7. If the factor outside the parenthesis is a positive number, the symbols of the items in the original parentheses are the same as the original symbols after the parentheses are removed;

8. If the factor outside the parenthesis is negative, the symbols of the items in the original parentheses are opposite to the original symbols after the parentheses are removed.

9. In general, several integers are added and subtracted, and if there are parentheses, the parentheses are removed first, and then similar terms are merged.

1. Multiple choice questions: (4 points per question, 32 points in total).

1. For the monomial, the coefficients and times are respectively ( ).

a.－2,2 b.－2,3 c. d.

2. In the following formulas, the same term as is ( ).

a． b．2xy c．－ d．

3. The number A is greater than 2 times the number of B 3, if the number B is x, then the number A is ( ).

a．2x－3 b． 2x+3 c． x－3 d． x+3

4. The opposite of is ( ).

a． b． c． d．

5. If , then it is ( ).

a. b. c. d.

6. The circumference of a rectangle is , and one side of it is long, and the other side is ( ).

a． b． c． d．

7. If the known value of is 3, then the value of algebraic is ( ).

a、0 b、－7 c、－9 d、3

8. If , then (

2. Fill-in-the-blank questions: (4 points per question, 16 points in total).

9. If it is the same kind of term, then m n

10. It is known that the single digit of a three-digit number is a, the ten-digit number is 3 times larger than the single-digit number, and the hundred-digit number is twice the one-digit number, and this three-digit number can be expressed as

11. Known:

1) In the second figure, the number of matches sticks is

2) In the third figure, the number of roots of the matchstick is:

3) In the 4th figure, the number of roots of the matchstick is:

4) In the nth figure, the number of roots of the matchstick is

18. The price of a note is one yuan, if you buy more than 100 copies (excluding 100 copies), the price is one yuan, and the column formula indicates the amount of money required to buy n notebooks (note that the size of n should be considered).

1) According to this price regulation, will there be a situation where buying more than buying less will pay less?

2) If I need 100 notebooks, how can I save money by buying them?

1)（ a2b）3•（-9ab3）÷（a5b3） (2)

3) (4) (2x＋y＋1)(2x＋y－1)

5) (6) （3xy－2x2－3y2）＋（x2－5xy＋3y2）

2.Simplify, then evaluate:

x+2)2-(x+1)(x-1), where x=

Thereinto. 3), where . .

4) (2a 3b)(3b 2a) (a 2b)2, where: a = 2, b = 3

3 Calculate in an easy way:

4.There is such a problem, calculate: the value of 2(x+y)(x y)+[x+y)2 xy]+ x y)2+xy], where x=2006, y=2007;A student mistakenly copied "y=2007" as "y=2070", but his calculation is correct, please answer what is going on?

Let's try to explain why.

Rationale:

Isn't it okay to come up with the questions yourself?

The addition and subtraction of integers is actually to remove parentheses and merge similar terms The general steps of integer addition and subtraction operations are: (1) remove brackets according to the law of removing brackets; (2) Accurately find out the same kind of items, and merge similar items according to the law of merging similar items

When solving the problem of finding the value of an algebraic formula, the addition and subtraction of the integer formula should be simplified first, that is, the parentheses with parentheses should be removed first, and then the similar terms should be combined, and finally the algebra values should be calculated

The types of questions related to the addition and subtraction of integers are generally comprehensive application problems combined with other knowledge, such as simplification of formulas containing absolute value symbols, evaluation problems that use the whole idea to substitute as a whole, and so on

So the answer is: remove the brackets; merging similar items; Homogeneous items; simplification; Substitution as a whole

Generally, several integers are added and subtracted, and if there are parentheses, the parentheses are removed first, and then the similar terms are merged

So the answer is: remove the brackets; merging similar items;

If there are brackets, remove the brackets first, and then merge the same kind of difficult items

Therefore, the answer is: to bracket the quiet sign; merging similar items;

The addition and subtraction of integers is actually to remove parentheses and merge similar terms The general steps of integer addition and subtraction operations are: (1) remove brackets according to the law of removing brackets; (2) Accurately find out the same kind of items, and merge similar items according to the law of merging similar items

When solving the problem of finding the value of an algebraic formula, the addition and subtraction of the integer formula should be simplified first, that is, the parentheses with parentheses should be removed first, and then the similar terms should be combined, and finally the algebra values should be calculated

The types of questions related to the addition and subtraction of integers are generally comprehensive application problems combined with other knowledge, such as simplification of formulas containing absolute value symbols, evaluation problems that use the whole idea to substitute as a whole, and so on

So the answer is: remove the brackets; merging similar items; Homogeneous items; simplification; Substitution as a whole

If parentheses.

It is preceded by " " to remove the parentheses, and the symbols in the parentheses remain unchanged:

If the parentheses are preceded by " " to remove the parentheses, the words in the parentheses will change, change.

It's the multiplicative distributive law, if the parentheses are preceded by " " is equivalent to multiplying the parentheses by +1, remove the parentheses, then you have to multiply each item by +1.

If the parentheses are preceded by " " is equivalent to multiplying the parentheses by -1, and removing the parentheses, then you need to multiply each item by -1.

For example: +(2a-3b-5c) = 2a-3b-5c, and for example: -(2a-3b-5c) = -2a+3b+5c.