Multiplication of algebraic expressions:
Including (monomial) and (monomial) multiplication; Multiply (a polynomial) by (a monomial); Multiply (a polynomial) by (a polynomial)
Algorithm of single item and single item multiplication: single item multiplication, respectively multiplied by their coefficients and the same letters. For letters contained only in a monomial, the exponent is taken as a factor of the product.
Multiplication law of algebraic expressions;
1, multiplied by the power of the same base:
Rule: multiply by the power of the base, the base is unchanged, and the index is added. Mathematical symbol: am.an=am+n (where m and n are positive integers)
2, the power of power:
Law: power, constant basis, exponential multiplication. Mathematical symbol: (am)n=amn (where m and n are positive integers)
3. Product power:
Rule: multiply the factors in the product and then multiply them by the power. (that is, equal to the product of the power of each factor in the product. )
Mathematical symbol: (ab)n=anbn (where n is a positive integer)
4. Multiplication of monomial and monomial:
Multiply their coefficients and the powers of the same letters respectively, and the remaining letters, together with their exponents, remain the same as the factors of the product.
5, single and polynomial multiplication:
Is to multiply each term of a polynomial by a single term 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 expression multiplication: the rule of multiplying monomial by monomial;
The monomial is multiplied by the monomial, and their coefficients and the power of the same letter are multiplied by the multiplicative commutative law and the associative law respectively, and the remaining letters and their exponents are used as the factors of the product.
Note: The multiplication of monomial and monomial is actually accomplished by using the law of multiplication and same base powers's arithmetic. The coefficient of the product of 1. is equal to the product of the coefficients of each factor. Determine the sign first, and then calculate the absolute value. At this time, the mistake that is easy to occur is to confuse coefficient multiplication with exponential addition.
For example, 2a3a2 = 6a5 instead of 6a6 or 5a5.
② Multiply the powers of the same letters by using the multiplication property of the powers of the same base.
(3) The letters only contained in the monomial should be taken as the factors of the product together with their exponents. (4) The multiplication rule of monomials is also applicable to the multiplication of more than three monomials. (5) The result of multiplying the monomial by the monomial is still the monomial. Algorithm of multiplying polynomial by monomial;
The multiplication of monomial and polynomial is to multiply each term of polynomial by monomial according to the law of multiplication and distribution, and then convert it into the multiplication of monomial and monomial, and then add the products obtained.
Rule: Multiply polynomials by multiplying each term of one polynomial by each term of another polynomial, and then add the products.
Methods Summary: When exploring the multiplication of polynomials, a polynomial is regarded as a whole and calculated by using the distribution law. Here again, the application of holistic thought in mathematics is explained.