计算 (x+3y-2z)(x-3y+2z)2 (a+b+c-2)(a+b-c+2)

问题描述:

计算 (x+3y-2z)(x-3y+2z)
2 (a+b+c-2)(a+b-c+2)

=[X+(3y-2z)][X-(3y-2z)]
=X^2-(3y-2z)^2
2(a+b+c-2)(a+b-c+2)=2[(a+b)+(c-2)][(a+b)-(c-2)]
=2[(a+b)^2-(c-2)^2]

平方差公式。

(x+3y-2z)(x-3y+2z)
=x²-(3y-2z)²
=x²-9y²-4z²+12yz
(a+b+c-2)(a+b-c+2)
=(a+b)²-(c-2)²
=a²+2ab+b²-c²+4c-4