Question

已知A=a^2+2b-3c^2+4 B=b^2-2c^2-3a^2 C=-5c^2-2a^2+3b 试说明A+B-C的值与a a c无关

Answer 1

解：A+B-C
=a²+2b-3c²+4+b²-2c²-3a²-(-5c²-2a²+3b)
=a²+2b-3c²+4+b²-2c²-3a²+5c²+2a²-3b,合并同类项
=b²-b+4
因为b²-b+4中没含有a与c的项，所以A+B-C的值与a,c无关

Answer 2

已知A= a^2+2b-3c^2+4 B=b^2-2c^2-3a^2 C=-5c^2-2a^2+3b 试说明A+B-C的值与a a c无关
A+B-C=(a^2+2b-3c^2+4)+(b^2-2c^2-3a^2 )-(-5c^2-2a^2+3b )
=(a^2-3a^2 +2a^2)+(2b-3b)+(-3c^2-2c^2+5c^2)+4+(b^2)
=-b+4+b^2=b^2-b+4