Question

计算 (3x-2y+z)(3x+2y-z)

Answer 1

（1）(3x-2y+z)(3x+2y-z)=[3x-(2y-z)][3x+(2y-z)]=(3x)^2-(2y-z)^2=9x^2-4y^2+4yz-z^2（2）(m-n+2p)(m+n-2p)=[m-(n-2p)][m+(n-2p)]=m^2-(n-2p)^2=m^2-n^2+4np-4p^2（3）(3m-n+1)(3m+n+1)=[(3m+1)-n][(3m+1)+n]=(3m+1)^2-n^2=9m^2+6m+1-n^2（4）(2x-y-3)(2x+y-3)=[(2x-3)-y][(2x-3)+y]=(2x-3)^2-y^2=4x^2-12x+9-y^2（5）(2a-3b-c)(2a+3b+c)=[2a-(3b+c)][2a+(3b+c)]=(2a)^2-(3b+c)^2=4a^2-9a^2-6bc-c^2