Question

（1）(9.5^2)+9.5+0.25简便运算 （2）分解因式（x²+1）²-10（x²+1）+25

详细点

Answer 1

解：⑴ 9.5^2+9.5+0.25
= 9.5^2+(9.5×0.5+9.5×0.5)+0.5×0.5
=9.5^2+9.5×0.5+9.5×0.5+0.5×0.5
=9.5×(9.5+0.5)+0.5×(9.5+0.5)
=9.5×10+0.5×10
=95+5
=100

⑵ （x²+1）²-10（x²+1）+25
=（x²+1）²-(5+5)（x²+1）+5×5
=（x²+1）²-5（x²+1）-5（x²+1）+5×5
=（x²+1）[（x²+1）-5] - 5[（x²+1）-5]
=[（x²+1）-5] × [（x²+1）-5]
=[（x²+1）-5]²
=(x²-4)²
PS:或者化简为：（x+2)²(x-2)²

Answer 2

（1）(9.5^2)+9.5+0.25简便运算
=9.5^2+2*0.5*9.5+0.5^2
=(9.5+0.5)^2
=100

（2）分解因式（x²+1）²-10（x²+1）+25
=(x^2+1-5)^2
=(x^2-4)^2
=(x+2)^2*(x-2)^2

Answer 3

(9.5^2)+9.5+0.25
＝﹙9.5﹚²＋9.5＋¼
＝﹙9.5＋½﹚²
＝﹙9.5＋0.5﹚²＝1
（x²+1）²-10（x²+1）+25 设x²＋1＝t
＝t²－10t＋25
＝﹙t－5﹚²
＝﹙x²＋1－5﹚²
＝﹙x²－4﹚²