If the number represented by a letter can take any value within a specified range, the value of the letter is said to be variable, and the letter represents a variable (or argument).

When omitting the multiplication sign, write the number before the letter. When a fraction is a mixed number, it is often written as an improper fraction.

An expression formed by connecting numbers or letters representing numbers using operational symbols and parentheses is called an algebraic expression.

A single number or letter is also an algebraic expression.

Replace the letters in the algebraic expression with numerical values, and according to the operational relationships in the algebraic expression, the calculated result is called the value of the algebraic expression.

An algebraic expression composed of the product of a number and a letter or the product of a letter and a letter is called a monomial.

The numerical factors in a monomial are called the coefficients of the monomial.

A single number is also a monomial.

In a monomial, the sum of the exponents of all letters is called the degree of the monomial.

An algebraic expression composed of the sum of several monomials is called a polynomial. Each monomial in a polynomial is called a term of the polynomial, and terms without letters are called constant terms. The degree of the highest term is the degree of the polynomial.

Monomials and polynomials are collectively called integers.

Monomials that contain the same letters and have the same prime numbers with the same letters are called homonomials.

Combining like terms in a polynomial into one term is called merging like terms. When a polynomial is combined and contains several terms, it is called a polynomial.

The result of adding the coefficients of similar items is used as the combined coefficient, and the letters and their exponents remain unchanged.

Before the brackets, remove the and brackets, and the items in the brackets will remain unchanged.

The parentheses are preceded by - and the parentheses are removed, and the signs of the items in the parentheses are changed.

Multiply powers with the same base, keep the base unchanged, and add the exponents.

When raising powers, the base remains unchanged and the exponents are multiplied.

The power of a product is equal to the power of each factor of the product, and then the resulting powers are multiplied together.

To multiply a monomial by a monomial, the product of multiplying their coefficients and powers with the same base is used as the factor of the product. The remaining letters, together with its exponent, remain unchanged and are also used as factors of the product.

Multiply monomials by polynomials, multiply the monomials by each term of the polynomial, and add the resulting products.

To multiply polynomials, first multiply each term of one polynomial by each term of the other polynomial, and then add the resulting products.

The product of the sum of two numbers and the difference of the two numbers is equal to the squared difference of the two numbers.

The square of the sum (or difference) of two numbers is equal to the sum of their squares plus (or minus) twice their product.

Converting a polynomial into the product of several integers is called factoring the polynomial, which is also called factoring the polynomial.

The factors contained in each term of a polynomial are called the common factors of the polynomial.

If each term of a polynomial contains a common factor, then the common factor can be extracted as a factor of the polynomial, and the formula after the common factor is put in brackets as another factor. This method of factoring is called the common factor extraction method.

The common factor extracted should be the product of the greatest common factor of the coefficients of each term (when the coefficients are all integers) and the lowest power of the same letter that each term contains.

The method of factoring a polynomial using the multiplication formula is called the formula method.

When factoring, be careful that the final result must be decomposed until it can no longer be decomposed.

It can be decomposed using the square difference formula and the perfect square formula.

The method of factoring quadratic trinomials by using cross lines to decompose coefficients is called the cross multiplication method.

The method of using groups to decompose factors is called group decomposition.

When powers with the same base are divided, the base remains unchanged and the exponents are subtracted.

Any number not equal to zero raised to the zero power is 1

To divide two monomials, divide the coefficients and powers with the same base respectively as factors of the quotient. For letters contained only in the dividend, use its exponent as a factor of the quotient.

To divide a polynomial by a monomial, first divide each term of the polynomial by the monomial, and then add the resulting quotients.