4a^2+4a+b^2-6b+10
=(4a^2+4a+1)+(b^2-6b+9)
=(2a+1)^2+(b-3)^2=0
∵(2a+1)^2≥0,(b-3)^2≥0,
∴2a+1=0,b-3=0
∴a=-1/2,b=3
∴a^3*b+a*b^3
=ab*(a^2+b^2)
=(-1/2)*3*[(-1/2)^2+3^2]
=-111/8