What are the basic concepts and formula rules in the first chapter of the second volume of seventh grade mathematics? Multiplication of algebraic expressions: including (monomial) and (monomial) multiplication; Multiply (a polynomial) by (a monomial); (Polynomial) Multiply with (Polynomial) Arithmetic of multiplying a monomial with a monomial: Multiply a monomial and multiply their coefficients with the same letter respectively. For letters contained only in the monomial, the exponent is taken as a factor of the product. ? Algebraic expression multiplication rule: 1, multiplied by the power of the base: rule: multiplied by the power of the base, the base is unchanged, and the exponents are added. Mathematical notation: am.an=am+n (where m and n are positive integers) 2. Power: law: power, constant radix, exponential multiplication. Mathematical notation: (am)n=amn (where m and n are positive integers) 3. Power of product: law: power of product, first multiply each factor in the product separately, and then multiply the obtained power. (that is, equal to the product of the power of each factor in the product. ) Mathematical notation: (ab)n=anbn (where n is a positive integer) 4. Multiplication of monomials: multiply their coefficients and the powers of the same letters respectively, and the remaining letters, together with their exponents, remain unchanged as the factors of the product. 5. Multiplication of polynomial and monomial: multiply each term of polynomial with monomial according to the distribution law, and then add the products. 6. Multiplication of polynomials: first multiply each term of one polynomial with each term of another polynomial, and then add the products. 7. Multiplication formula: square difference formula: (a+b) (a-b) = A2-B2, complete square formula: (a+b)2=a2+2ab+b2, (a-b)2=a2-2ab+b2. ? Algebraic multiplication: the rule of multiplying a monomial by a monomial: the monomial is multiplied by the monomial, their coefficients and the powers of the same letters are multiplied by the multiplicative commutative law and the associative law respectively, and the remaining letters together with their exponents are taken as the factors of the product. Note: The multiplication of monomial by monomial is actually completed by using the law of multiplication and the power operation of the same base number. (1) the coefficient of the product is equal to the product of each factor coefficient, first determine the symbol, and then calculate the absolute value. At this time, the common mistake is to confuse coefficient multiplication with exponential addition, for example, 2a3A2 = 6a5, instead of thinking that it is a power multiplication of 6a6 or 5a5. ② The multiplication property of the same base power is used. (3) letters only contained in the monomial, take its index as a factor of the product. ④ The multiplication rule of monomials is also applicable to the multiplication of more than three monomials. ⑤ When a monomial is multiplied by a monomial, the result is still a monomial. Arithmetic of multiplying polynomial by monomial: The arithmetic of multiplying polynomial by monomial is to multiply each term of polynomial by monomial according to the law of multiplication and distribution, and then add the obtained products. Multiply each term of one polynomial by each term of another polynomial, and then add the products. Method summary: When discussing the multiplication of polynomials, we regard a polynomial as a whole and use the distribution law to calculate it. Here, we once again explain the application of holistic thought in mathematics.