①；已知a+b=4,ab=3,求a³b-a²b²+ab³的值
a³b-a²b²+ab³
=ab(a²-ab+b²)
=ab[(a+b)²-3ab]
=3(4²-3*3)
=3*7
=21
②；如果多项式4x²+mx+25是完全平方式,求m的值
4x²+mx+25
=(2x+5)²
=4x²+20x+25
m=20
③；已知a²+b²+4a-2b+5=0,求a,b的值
a²+b²+4a-2b+5=0
a²+4a+4+b²-2b+1=0
(a+2)²+(b-1)²=0
a+2=0
a=-2
b-1=0
b=1
④；已知x-y=4,y-z=2,求x²y+y²z+z²x-(xy²+yz²+zx²)
x²y+y²z+z²x-(xy²+yz²+zx²)
=x²y-xy²+y²z-yz²+z²x-zx²
=xy(x-y)+yz(y-z)+xz(z-x)
=4xy+2yz+xz(z-x)
x-y=4
x=4+y
y-z=2
y=2+z (1)
x=6+z (2)
把(1)(2)代入上式
原式=4(6+z)(2+z)+2(2+z)z+(6+z)z(z-6-z)
=4(12+8z+z²)+4z+2z²-6z(6+z)
=48+32z+4z²+4z+2z²-36z-6z²
=48
⑤；已知(a+b)²=8,(a-b)²=4,求a²+b²和ab的值
(a+b)²-(a-b)²
=a²+2ab+b²-a²+2ab-b²
=4ab
=8-4
=4
ab=1
(a+b)²=8
a²+b²+2ab=8
a²+b²=8-2ab
=8-2*2
=4
⑥；先化简,再求值：[(x-y)²+(x+y)(x-y)]除以2x,其中x=3,y=-1.5
[(x-y)²+(x+y)(x-y)]/2x
=(x²-2xy+y²+x²-y²)/2x
=(2x²-2xy)/2x
=[2x(x-y)]/2x
=x-y
把x=3,y=-1.5代入上式
原式=3-(-1.5)
=4.5