将下列多项式因式分解:(1) (z²-x²-y²)²-4x²y² (2) (a+b)²+
来源:学生作业帮助网 编辑:作业帮 时间:2024/10/06 19:38:47
xPJ1~AӥCAd!cdKzQ,xoc`xQꡁdo~ izjvi.k]S2
ФhDPCv<ӳbG;kN?,ܘk%cMNAgl>0aȓـL#zn-L^Rz)aCQ4JT9H*! D
IiB+۔!ɂIP`:'&D
将下列多项式因式分解:(1) (z²-x²-y²)²-4x²y² (2) (a+b)²+
将下列多项式因式分解:(1) (z²-x²-y²)²-4x²y² (2) (a+b)²+
将下列多项式因式分解:(1) (z²-x²-y²)²-4x²y² (2) (a+b)²+
因式分
(1) (z²-x²-y²)²-4x²y²
=(z^2-x^2-y^2-2xy)(z^2-x^2-y^2+2xy)
=[z^2-(x+y)^2][z^2-(x-y)^2]
=(z-x-y)(z+x+y)(z-x+y)(z+x-y) .
(z²-x²-y²)²-4x²y²
=(z^2-x^2-y^2-2xy)(z^2-x^2-y^2+2xy)
=[z^2-(x+y)^2][z^2-(x-y)^2]
=(z-x-y)(z+x+y)(z-x+y)(z+x-y) .
令A=x2、B=y2、C=z2
(C-A-B)2-4AB=A2+B2+C2-2CA-2AB-2BC+4AB
= A2+B2+C2-2CA+2AB-2BC=(A+B-C)2
=(x2+y2-z2)2