作业帮已知x=1/2a+1,y=1/2a+2,z=a-3,求x^2+2xy+y^2-2xz+z^2-2yz的值.
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已知x=1/2a+1,y=1/2a+2,z=a-3,求x^2+2xy+y^2-2xz+z^2-2yz的值.
已知x=1/2a+1,y=1/2a+2,z=a-3,求x^2+2xy+y^2-2xz+z^2-2yz的值.
已知x=1/2a+1,y=1/2a+2,z=a-3,求x^2+2xy+y^2-2xz+z^2-2yz的值.
x^2+2xy+y^2-2xz+z^2-2yz
=（X+Y)^2+Z(z-2x-2y)
=（X+Y)^2+Z[z-2(x+y)]
=（1/2a+1+1/2a+2)^2+(a-3)[a-3-2(1/2a+1+1/2a+2)]
=（a+3)^2+(a-3)[a-3-2(a+3)]
=（a+3)^2+(a-3)(-a-9)
=a^2+6a+9-a^2-6a+27
=36