请化简:a方乘以(b方加c方减a方)加b方乘以(a方加c方减b方)等于c方乘以(a方加b方减c方)

问题描述:

请化简:a方乘以(b方加c方减a方)加b方乘以(a方加c方减b方)等于c方乘以(a方加b方减c方)

a2(b2+c2-a2)+b2(a2+c2-b2)=c2(a2+b2-c2)
a2b2+a2c2-a4+a2b2+b2c2-b4=a2c2+b2c2-c4
a2b2.+a2c2-a4+a2b2+b2c2-b4-a2c2-b2c2+c4=0
2a2b2=a4+b4-c4
(a2-b2)2-c4=0
(a2-b2+c2)(a2-b2-c2)=0