1 and the multiplication of the same radix power.
(1) in general, a m = (aa aa aa) (ma is a positive integer), a n = (aa aa aa aa) (n a times, n
We draw the following conclusions: the law of multiplication with the same base power: multiply with the same base power, the base number is unchanged, and the exponents are added.
(2) A M = (A A A A A A A A A) (M A is a positive integer), A N = (A A A A A A A A A) (N A is a positive integer), (.
We have come to the following conclusion: (the power law of the same base power).
Power, constant radix, exponential multiplication.
(3) Generally speaking, A N = (A A A A A A A A A A) (N A is a positive integer), B N = (B B B B B B B B B) (N B is a positive integer), (N B is a positive integer).
We have come to the following conclusion: the power law of product: the power of product is equal to multiplying each factor of product respectively, and then multiplying the obtained power.
2. Multiplication of monomials.
(1) Multiplication rule of single item and single item: Single item and single item are multiplied by their coefficients and the same base respectively, and the remaining letters and their exponents remain unchanged as the factors of the product.
For example: (-6ab) x (-5ab) = 30ab.
(2) Multiplication rule of monomial and polynomial: Multiplying monomial and polynomial means multiplying each term of polynomial with monomial, and then adding the products.
For example: (-2xy-y) x (xy) =-2xy-xy.
3. Multiplication of polynomials.
(1) Polynomial Multiplication Rule: Multiply polynomials, multiply each term of one polynomial with each term of another polynomial, and then add the products.
For example: (x-y) x (x+y) = x-xy+xy-y = x-y.
(Note: If there are similar items in the results of polynomial multiplication, they should be merged. )。
4. multiplication formula.
(1) square difference: the product of the sum of two numbers and the difference of two numbers is equal to the square difference of these two numbers.
(a+b)x(a-b)=a-b .
(2) Complete sum of squares: the square of the sum of two numbers is equal to the sum of the squares of these two numbers, plus twice the product of these two numbers.
(a+b) = a+2ab+B. Complete square difference: the square of the difference between two numbers is equal to the sum of the squares of these two numbers, minus twice the product of these two numbers.
(a-b)=a-2ab+b .
5. The division of power with the same base.
(1) In general, A M =(A A A A A A A A)(M A is a positive integer) and an n = (aa aa aa aa) (n a times, n n.).
We have come to the following conclusion: (the division rule of the same radix power).
Same base powers divides, the base remains the same, and the exponent is subtracted.
a^m/a^n=a^m-n。 (a≠0, m and n are positive integers, m >；; n).
It is stipulated that the zeroth power of any number that is not equal to zero is equal to one.
a^0= 1(a≠0)。
The power of -n(n is a positive integer) of any number that is not equal to zero is equal to the reciprocal of the power of n of this number.
A-n =1/an n (a ≠ 0, n is a positive integer).
6. Division of algebraic expressions.
(1) Division rule of single item and single item: Multiply the single item, divide it by the coefficient and the same base as the factor of quotient, and take the letters only included in the division formula as the factor of quotient together with their indices.
For example: axy/2xy =ax/2y(x≠0, y≠0).
(2) Division rules of polynomials and monomials: polynomials are divided by monomials, each term of polynomials is divided by monomials first, and then the obtained quotients are added.
For example: (a+b+c)/n = a/n+b/n+c/n (n ≠ 0).
References:
Baidu Encyclopedia-Introduction to Mathematics in Senior One (II): Multiplication and Division of Algebraic Expressions