Question

若x+y=3,且（x+2）（y+2）=12 （1）求x²y+xy的值 （2）求x²+3xy+y²的

Answer 1

由题意得
12=(x+2)(y+2)
=xy+2(x+y)+4
=xy+2×3+4
=xy+10
所以 xy=12-10=2
(1)x²y+xy²=xy(x+y)=3×2=6
(2)x²+3xy+y²
=（x²+y²)+3×2
=(x+y)²-2xy+6
=3²-2×2+6
=11

Answer 2

你好~首先去掉括号化简2（x²y+xy）-3（x²y-xy）-4x²y=2x²y+2xy-3x²y+3xy-4x²y=2x²y-3x²y-4x²y+2xy+3xy=-5x²y+5xy=5xy(-x+1)=5(-1)(1)(1+1)=-10祝你学习进步

Answer 3

（x+2）（y+2）=xy+2（x+y）+4=xy+2*3+4=12
得xy=2
（1）x²y+xy²=xy（x+y）=2*3=6 ps：我怀疑你打错
（2）x²+3xy+y²=（x+y）²+xy=3²+2=11

Answer 4

（x+2）（y+2）=12
xy+2x+2y+4=12
xy+2（x+y）+4=14
xy+2×3+4=14
xy=4

x²y+xy²
=xy（x+y）
=4×3
=12

x²+3xy+y²
=x²+2xy+y²+xy
=（x+y）²+xy
=3²+4
=13