①（a+b）²-12（a+b)+36；②4x²+4x(m+n)+(m+n)²

①（a+b）²-12（a+b)+36；②4x²+4x(m+n)+(m+n)²

Factorization
①（a+b）²-12（a+b)+36
=(a+b-6)²
②4x²+4x(m+n)+(m+n)²
=（2x）²+4x(m+n)+(m+n)²
=(2x+m+n)²
Tip: use the complete square formula, combined with the whole idea, factorization

If the algebraic formula 4x & # 178; - 12x + M can be replaced by (2x-n) &# 178; + 1, the value of M and N can be obtained

4x²-12x+m
=(2x-3)²+m-9=（2x-n）²+1
3=n
m-9=1
∴m=10
n=3

If the point (m, n) is on the line 4x + 3y-10 = 0, then the minimum value of M2 + N2 is ()
A. 2B. 22C. 4D. 23

The point (m, n) is the closest point from the straight line to the origin. The straight line and two axes intersect at a (52, 0), B (0103). In the right triangle OAB, OA = 52, OB = 103, hypotenuse AB = (52) 2 + (103) 2 = 256, the height h on the hypotenuse is the arithmetic square root of M2 + N2, ∵ OAB area = 12 × OA × ob = 1