1.x²-4xy+4y²-10x+20y+25
=(x^2-4xy+4y^2)-(10x-20y)+25
=(x-2y)^2-10(x-2y)+25
=(x-2y-5)^2
2.(n+1)(n+2)(n+3)(n+4）+1
=[(n+1)(n+4)][(n+2)(n+3)]+1
=(n^2+5n+4)(n^2+5n+6)+1
=(n^2+5n)^2+10(n^2+5n)+24+1
=(n^2+5n)^2+10(n^2+5n)+25
=(n^2+5n+5)^2
填空题
当x=_______时,代数式x²-4x+10有最小值,最小值是_______
x^2-4x+10=(x^2-4x+4)+6
=(x-2)^2+6
因为(x-2)^2≥0
所以当(x-2)^2=0时,即x=2时,代数式x²-4x+10有最小值,最小值是6