关于整式1.若y-2的绝对值加(x-1)^2等于0.求代数式x的立方减x^2乘以y加xy^2加x^2乘以y减xy^2-y^3的值.2.若A=a^2+5b^2-4ab+2b+100.求A的最小值.3.已知a-b=2,b-c=2,a+c=14,求a^2-b^2.4.已知x-y=1,求x^2-y^2+x-3y的值.

Question

关于 整式
1.若y-2的绝对值加(x-1)^2等于0.求代数式x的立方减x^2乘以y加xy^2加x^2乘以y减xy^2-y^3的值.
2.若A=a^2+5b^2-4ab+2b+100.求A的最小值.
3.已知a-b=2,b-c=2,a+c=14,求a^2-b^2.
4.已知x-y=1,求x^2-y^2+x-3y的值.

Answer 1

1]
|y-2|+(x-1)^2=0
=>y-2=0&x-1=0
=>y=2&x=1
x^3-x^2*y+xy^2+x^2*y-(xy^2-y^3)
=x^3+y^3=1+8=9
2]
A=(a^2-4a+4b^2)+(b^2+2b+1)+99=(a-2b)^2+(b+1)^2+99
所以b=-1,a=-2时,A(min)=99
3]
b-c=2,a+c=14=>a+b=14+2=16
a^2-b^2=(a+b)(a-b)=16*2=32
4]
x-y=1=>x=y+1
x^2-y^2+x-3y
=(y+1)^2-y^2+(y+1)-3y
=y^2+2y+1-y^2+y+1-3y
=2