(x-y)(y-x)=?(-b-a)(a+b)=?(x-y)()=X的2次方-2xy+y的2次方计算(-3x-2y+z)(-3x-2y+z)

Question

(x-y)(y-x)=?
(-b-a)(a+b)=?
(x-y)( )=X的2次方-2xy+y的2次方
计算
(-3x-2y+z)(-3x-2y+z)

Answer 1

(x-y)(y-x)=xy-y^2-x^2+xy=-x^2+2xy-y^2
(-b-a)(a+b)=-(b+a)(a+b)=-(a^2+2ab+b^2)=-a^2-2ab-b^2
(x-y)(x+y)=X的2次方-2xy+y的2次方 由平方差公式得
(-3x-2y+z)(-3x-2y+z)
=-(3x+2y-z)×-(3x+2y-z)
=(3x+2y-z)(3x+2y-z)
=9x^2+6xy-3xz+6xy+4y^2-2yz-3xz-2yz+z^2
=9x^2+12xy-6xz+4y^2-4yz+z^2