Note: In (a-b)? =a? -3a? b+3ab? -B? In, its number is "+,-". +,-"after the first letter is arranged, and it is a homogeneous formula (3 times for each term), and its coefficients are 1, -3, +3,-1, and the result is a quartic formula.
Decomposition process of cubic formula;
The difference between two numbers multiplied by the sum of their squares and the sum of their products is equal to the cube of the difference between two numbers.
(a-b)? =a? -3a? b+3ab? -B?
So a? -B? =(a-b)? -[-3(a? )b+3ab? ]=(a-b)(a-b)? +3ab(a-b)
=(a-b)(a? -2ab+b? +3ab)=(a-b)(a? +ab+b? :
( 1)a? +b? =(a+b)(a? -ab+b? )。
(2)a n+b n =(a+b)[a(n- 1)-a(n-2)×b+...+(- 1) (r- 1 )× a(。