Same base powers's multiplication: the base is constant, and the exponents are added.

a^m？ A n = a Mn (m and n are positive integers)

Power: constant radix, exponential multiplication.

(a m) n = a Mn (m both m and n are positive integers)

Power of product: multiply each factor of the product separately, and then multiply the obtained power.

(ab)^n=a^n？ B n (n is a positive integer)

Multiplication of monomial and monomial: take the product of its coefficient and the same base as the factorial of the product, and other letters together with their exponents are also the factorial of the product.

Multiplication of monomial and polynomial: each term of polynomial is multiplied by monomial, and then the products are added.

Polynomial multiplication: Multiply each term of one polynomial by each term of another polynomial, and then add the products.

Attachment: Calculation: (x+y) 2? (x-y)^2

Solution: Original formula = [(x+y) (x-y)] 2

=(x^2-y^2)^2

=x^4-2x^2y^2+y^4

Factorization:

Extraction method of common factor: If every term of a polynomial contains a common factor, the common factor can be extracted as one factor of the polynomial, and the formula after the common factor is put in brackets as another factor.

Step: 1. Extract the greatest common factor of each coefficient.

2. Each item contains the same letter.

3. The lowest power of the same letter

Formula method:

Square difference of factorization: a 2-b 2 = (a+b) (a-b)

Features: Polynomials are binomials, each term is in the form of a certain number or the square of algebraic expression, and the coefficient signs of the two terms are different.

The complete square of factorization: A2+2ab+B2 = (a+b) 2a2-2ab+B2 = (a-b) 2.

Features: Polynomial is a trinomial, in which two terms are the squares of two algebraic expressions and one term is twice the product of these two algebraic expressions.

Cross multiplication: Using the crosshair to decompose the coefficient is a method to decompose the quadratic trinomial.

x^2+(a+b)x+ab=(x+a)(x+b)

Step: 1. Split constant term

2. Verify the project once.