Question

计算题：(a-b+c)(b-a+c)= （2a-b-c）^2= (a-3)(a^2+9)(a+3)=

Answer 1

(a-b+c)(b-a+c)

=[c+(a-b)][c-(a-b)]

=c^2-(a-b)^2

=c^2-(a^2-2ab+b^2)

=c^2-a^2+2ab-b^2

（2a-b-c）^2

=(2a)^2+b^2+c^2-2*2a*b-2*2a*c+2bc

=4a^2+b^2+c^2-4ab-4ac+2bc

(a-3)(a^2+9)(a+3)

=(a-3)(a+3)(a^2+9)

=(a^2-9)(a^2+9)

=a^4-81