1. Single item

An algebraic expression consisting of the product of numbers and letters is called a monomial. A single number or letter is also a monomial.

(2) The coefficient of a single item is a numerical factor of a single item. As a coefficient of a monomial, the number must be preceded by an attribute symbol. If the monomial is just a product of letters, it is not without coefficients.

(3) In a monomial, the index sum of all letters is called the number of times of the monomial.

2.polynomial

The sum of several monomials is called polynomial. In polynomials, each monomial is called a polynomial term.

Among them, items without letters are called constant items. The degree of the term with the highest degree in a polynomial is called the degree of the polynomial.

② Both monomials and polynomials have degrees, while monomials with letters have coefficients and polynomials have no coefficients. Every term of a polynomial is a monomial, and the number of terms of a polynomial is the number of monomials with the polynomial as the addend. Each term in a polynomial has its own degree, but their degrees cannot all be regarded as the degree of this polynomial. A polynomial has only one degree, which is the highest degree of the contained terms.

3. Algebraic expression

Algebraic expressions monomials and polynomials are collectively called algebraic expressions.

Second, the addition and subtraction of algebraic expressions

The addition and subtraction of 1. algebraic expression is essentially the combination of similar items after removing brackets, and the operation result is a polynomial or a single item.

There is a "-"sign before the brackets. When the brackets are deleted, the symbols of the items in the brackets should be changed. When a number is multiplied by a polynomial, the number should be multiplied by the items in brackets.

Third, the same base power multiplication.

Law of multiplication with the same base and power;

(m, n are all positive numbers) is the most basic rule in the operation of power.

When applying this algorithm, we should pay attention to the following points:

① The preconditions for using this rule are: when the bases of powers are the same and multiplied, the base a can be a specific numeric letter or a term or polynomial;

② When the index is 1, don't mistake it for no index;

③ Don't confuse multiplication with addition of algebraic expressions. Multiplication, as long as the base is the same, the indexes can be added; For addition, not only the radix is the same, but also the exponent needs to be added;

(4) When three or more identical base powers are multiplied, the rule can be summarized as follows.

(where m, n and p are all positive numbers);

⑤ The formula can also be reversed:

(m and n are positive integers).

Fourth, the power of power and the power of products.

1. power law:

(m, n are both positive numbers) is derived from the multiplication rule of powers, but the two cannot be confused.

2.

3.？ When the base has a negative sign, it should be noted that when the base is a and (-a), it is not the same base, but it can be transformed into the same base by power law, such as:

Convert to:

4.？ The base sometimes has different forms, but it can be replaced with the same one.

5. Pay attention to the difference between the n power of (ab) and the n power of (a+b).

6. Power law of product: the power of product is equal to each factor of product multiplied by power respectively, and then multiplied by the obtained power, namely:

(n is a positive integer).

7. Power and product power rules can be applied in reverse.

Five, the same base power division

1. same base powers's division rule: same base powers divides, the base number remains the same, and the exponent is subtracted, that is:

(a≠0, m, n is positive, m >；; n).

2. In application, the following points should be noted:

(1) The premise of using the rule is "same base powers division" and 0 is not divisible, so a ≠ 0 in the rule;

② Any number not equal to 0, whose power of 0 is equal to1;

③ The -p power of any number not equal to 0 (p is a positive integer) is equal to the reciprocal of the power of this number, that is, (a≠0, p is a positive integer).