Question

几道数学题目，挺多的。求一一回答。求好心人回答 1

[A+B][X+Y]-[B+A][Y-X]
144[A-B]^2-225]A+B]^2
A^2B^2+4-4AB
XY^2-4X^2-十六分之一Y^4
[M^2+2m]^2-2m+4n^2]^2
上面都是因式分解。下面是简便
73×145^2-105^2×73
1000^2
下面是计算
[2X-Y][X^2+XY-2Y^2]
2005^2-2004×2006

Answer 1

1.(A+B)(X+Y)-(B+A)(Y-X)=(A+B)[(X+Y)-(Y-X)]=(A+B)(X+Y-Y+X)=2X(A+B)
2.144(A-B)^2-225(A+B)^2=[12(A-B)]^2-[15(A+B)]^2=[12(A-B)-15(A+B)][12(A-B)+15(A+B)]=
(-3A-27B)(27A+3B)=-(3A+27B)(27A+3B)
3.A^2B^2+4-4AB=(AB)^2-2·2AB+2^2=(AB-2)^2
4.XY^2-4X^2-Y^4/16=-4X^2+XY^2-Y^4/16=-(4X^2-XY^2+Y^4/16)=-[(2X)^2-XY^2+(Y^2/4)^2]=
-(2X-Y^2/4)^2
5.[m^2+2m]^2-2m+4n^2]^2=[m^2+2m]^2-2m+4n^2]^2
上面都是因式分解。
下面是简便运算。
73×145^2-105^2×73=73(145^2-105^2)=73(145-105)(145+105)=73×40×250=730000
1000^2=1000000=10^6
下面是计算
[2X-Y][X^2+XY-2Y^2]=
2005^2-2004×2006=2005^2-(2005-1)*(2005+1)
=2005^2-2005^2+1
=1