1 until it can no longer be decomposed. (Note that the conclusions drawn according to different standards are different), such as:

Factorization in the range of rational numbers;

x^4- 4=(x^2)^2-2^2=(x^2+2)(x^2-2)

Factorization in the range of real numbers;

x^4- 4=(x^2)^2-2^2=(x^2+2)(x^2-2)=(x^2)(x+√2)(x-√2)

2. Two terms: extraction or square difference formula,

Three terms: extraction, complete square formula, cross multiplication, more than four terms, group decomposition,

3.( 1) satisfies three items, and (2) satisfies: the first square and the last square, with the first and last squares placed twice in the middle.

4、⑴4m^2(2x-3y)^2-m^2(3x-2y)^2

= m 2 [4 (2x-3y) 2-(3x-2y) 2] (first extract m 2, then treat it as two items as a whole, and use the square difference formula).

=m^2(4X-6Y+3X-2Y)(4X-6Y-3X+2Y)

=m^2(7X-8Y)(X-4Y)

⑵4m^2(2x-3y)^2-m^2(3x-2y)^2

= [2m (2x-3y)] 2-[m (3x-2y)]

= [2m (2x-3y)+m (3x-2y)] [2m (2x-3y)-m (3x-2y)] (Then extract m separately, and then do the same. )