1.
a(a-b)+b(b-a)
=a(a-b)-b(a-b)
=(a-b)²
=4²
=16
2.
任意非零实数的0次方=1
a- 1/2≠0
a≠1/2
a的取值范围是(-∞,1/2)U(1/2,+∞)
3.
m³n+2m²n²+mn³
=mn(m²+2mn+n²)
=mn(m+n)²
=(2/3)·3²
=6
4.
-a²b-ab²=-ab(a+b)=-2·3=-6
5.
2a³b²+a²b³
=a²b²(2a+b)
=(ab)²(2a+b)
=8²·(1/8)
=8
6.
a²b+ab²=ab(a+b) /怀疑你抄错题了,a²应该是a²b
=2·3
=6
7.
x+5z=5y
x=5y-5z=5(y-z)
x²-25y²+4z²+4xz
=[5(y-z)]²-25y²+4z²+4[5(y-z)]z
=25y²-50yz+25z²-25y²+4z²+20yz-20z²
=9z²-30yz,与y、z的取值有关,因此不是定值.怀疑你又抄错题了.应该是x+2z=5y
如果是x+2z=5y,那么：
x²-25y²+4z²+4xz
=(x²+4xz+4z²)-25y²
=(x+2z)²-(5y)²
=(x+2z+5y)(x+2z-5y)
=(x+2z+5y)·0
=0,为定值0
8.
任意非零实数的0次方=1
2x-3≠0
x≠3/2
x的取值范围是(-∞,3/2)U(3/2,+∞)
9.
1/10 化为相同底数
10.
x^m ·x^n=x^4 x^(m+n)=x^4
m+n=4 (1)
x^m÷x^n=x^8 x^(m-n)=x^8
m-n=8 (2)
[(1)+(2)]/2
m=6
[(1)-(2)]/2
n=-2
mn=8·(-2)=-16
11.
2^m=a 2^n=b
2^(m-n)=2^m /2^n=a/