(x-3y+2z)(-x-3y-2z)=?

问题描述:

(x-3y+2z)(-x-3y-2z)=?

原式=(-3y+(x+2z))*(-3y-(x+2z))
=(-3y)²-(x+2z)²
=9y²-(x²+4z²+4z)
=9y²-x²-4z²-4z

(x-3y+2z)(-x-3y-2z)
=-(x-3y+2z)(x+3y+2z)
=-[(x+2z)-3y][(x+2z)+3y]
=-[(x+2z)^2-9y^2]
=-x^2-4xz-4z^2+9y^2

(-3y+x+2z)[-3y-(x+2z)]
=(-3y)²-(x+2z)²
=9y²-x²-4z²-4xz

-x^2-4xz+9y^2-4z^2
没问题

运用平方差公式
(x-3y+2z)(-x-3y-2z)
=-(x-3y+2z)(x+3y+2z)
=-[(x+2z)-3y][(x+2z)+3y]
=-[(x+2z)²-9y²]
=-x²-4xz-4z²+9y²