陈丹青油画步骤:化简:(a+b)^2(b+c-a)(c+a - b)+(a - b)^2(a+b+c)(a+b - c)

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(a+b)^2(b+c-a)(c+a - b)+(a - b)^2(a+b+c)(a+b - c)
=(a+b)^2[c-(a-b)][c+(a-b)]+(a - b)^2[(a+b)+c][(a+b)-c]
=(a+b)^2[c^2-(a-b)^2]+(a - b)^2[(a+b)^2-c^2]
=(a+b)^2 c^2-(a+b)^2(a-b)^2+(a - b)^2 (a+b)^2-(a - b)^2 c^2
=(a+b)^2 c^2-(a - b)^2 c^2
=c^2[(a+b)^2-(a - b)^2]
=4ab c^2

(a+b)^2(b+c-a)(c+a - b)+(a - b)^2(a+b+c)(a+b - c)
=(a+b)^2[c-(a-b)][c+(a-b)]+(a - b)^2[(a+b)+c][(a+b)-c]
=(a+b)^2[c^2-(a-b)^2]+(a - b)^2[(a+b)^2-c^2]
=(a+b)^2 c^2-(a+b)^2(a-b)^2+(a - b)^2 (a+b)^2-(a - b)^2 c^2
=(a+b)^2 c^2-(a - b)^2 c^2
=c^2[(a+b)^2-(a - b)^2]
=4ab c^2