What is the operation of an integer?

Integer operations refer to the addition, subtraction, and multiplication of integers. Addition and subtraction are mainly to merge similar terms, and multiplication is divided into a variety of cases:

There are monomial multiplication, monomial multiplied by polynomial, polynomial multiplied by polynomial, and it is especially pointed out that the commonly used polynomial multiplied by polynomial appears as a perfect square formula and a square difference formula, which needs to be remembered.

Subtraction formula1. Minus - minus = difference.

2. Difference + subtraction = subtraction.

3. Minus - difference = minus.

Subtraction-related properties.

1. Anti-exchange rate: subtraction is anti-exchange, if a and b are any two numbers, then (a-b)=-b-a).

2. Anti-associativity: Subtraction is anti-associative, and when trying to redefine subtraction, then a-b-c=a-(b+c).

An integer operation is an operation in which the denominator does not contain an unknown number.

Integer is a general term for monomial and polynomial, which is a part of rational expression, in which it can contain five operations: addition, subtraction, multiplication, division, and multiplication, but in the integer, the divisor cannot contain letters.

Addition, subtraction, multiplication and division:

The addition and subtraction of the mononomial formula is to merge the same terms, that is, the sum of the coefficients of the same terms before the merger, and the letters remain unchanged. Multiply the monomials, multiply their coefficients, the same letters, and for the letters contained in only one monomial, together with its exponents, as a factor of the product.

In polynomials, each monomial is called the term of the polynomial, where the term without a letter is called a constant term. A polynomial is called a polynomial when there are several terms of the same kind. The symbols in polynomials are regarded as the property symbols of the terms. Unary nth order polynomials have a maximum of n+1 terms.

The number of polynomials is the number of terms with the highest order, not the sum of the terms of terms, and it is clear whether it is a falling power or an ascending power arrangement, and both the descending and ascending powers are sorted by a certain letter (unknown quantity). Multiply a monomial by multiplying their coefficients and powers of the same base, and for a letter contained in only one monomial, together with its exponent, as a factor of the product.

Sibling operations are counted from left to right (left to right). Heterogeneous operations are followed by two (second level operations first, then first level one operations, second level, + is first level). The ones with parentheses are first inside and then outside (the ones in the brackets are counted first, and then the ones outside the brackets are counted).

There are two reasons: one is that you are not careful enough.

The second is that you don't know the algorithm of integers well, so you will make mistakes when doing it.

Workaround:

1. Memorize the integer algorithms one by one (mainly to understand the rules), so that you can write them silently.

2. Create a mistake book and copy the questions you did wrong before. After memorizing the algorithm, redo these questions twice before the mid-term exam (not twice, of course, but once and again a week or two later).

Monomial. and polynomials are collectively referred to as integers.

Algebraic formula. A rational formula in . There are no division operations or fractions, and division operations and fractions, but division or denominators.

If there are no variables, it is called an integer.

Integers can be divided into definitions and operations, definitions can be divided into monomials and polynomials, and operations can be divided into addition, subtraction, and multiplication and division.

Addition and subtraction include the merging of similar items.

Multiplication and division include basic operations, rules and formulas, and basic operations can be divided into power operation properties, rules can be divided into integers, dividing commas and formulas can be divided into multiplication formulas.

Exponential power of zero and exponential power of negative integers.

1. Four operations of integers.

Addition and subtraction of integers.

Merging similar items is the key point, but it is also the difficulty. The following three points should be paid attention to when merging similar items: To grasp the concept of similar terms, be able to identify similar terms, and accurately grasp the two standard letters and letter exponents for judging similar terms; It is clear that the meaning of merging terms of the same kind is to merge the terms of the same kind in the polynomial into one, and after merging the terms of the same kind, the number of terms of the polynomial will be reduced, so as to achieve the purpose of simplifying the polynomial; "Merge" refers to the addition of the coefficients of the same term, and the result is taken as a new coefficient, keeping the letters and exponents of the same terms unchanged.

Multiplication and division of integers.

The focus is on multiplication and division of integers, especially the multiplication formulas in them. The structural features of multiplication formulas, as well as the broad meanings of the letters in the formulas, are not easy for students to grasp. Therefore, the flexible use of multiplication formulas is a difficulty, and the handling of symbols in parentheses is another difficulty when adding (or removing parentheses).

Parentheses (or deparentheses) are variations of polynomials that are performed according to the law of parentheses (or parentheses). In multiplication and division of integers, multiplication and division of monomials is the key, because the multiplication and division of general polynomials are "transformed" into multiplication and division of monomials.

The main types of integer four-rule operations are:

1) Four operations of a monomial.

Most of these questions are in the form of multiple-choice questions and application questions, which are characterized by the examination of the four operations of a single manuscript mega.

2) Operations on monomials and polynomials.

Most of these questions are in the form of burying and selling solution questions, which are highly skillful, and they are characterized by the examination of four operations of mononomials and polynomials.

Solution: Original formula = -2x y -(8x y) -4xy 8x y -2x y -4xy

Idea: Use the multiplicative distributive property to multiply -4xy by each term in parentheses to get the result. However, the simplified equation cannot combine similar terms, so the final answer can only be 8x y -2x y -4xy).

Hope you can o(o】