将下列多项式因式分解:(1) (z²-x²-y²)²-4x²y² (2) (a+b)²+
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![将下列多项式因式分解:(1) (z²-x²-y²)²-4x²y² (2) (a+b)²+](/uploads/image/z/430786-10-6.jpg?t=%E5%B0%86%E4%B8%8B%E5%88%97%E5%A4%9A%E9%A1%B9%E5%BC%8F%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%9A%EF%BC%881%EF%BC%89+%EF%BC%88z%26%23178%3B-x%26%23178%3B-y%26%23178%3B%EF%BC%89%26%23178%3B-4x%26%23178%3By%26%23178%3B+%EF%BC%882%EF%BC%89+%EF%BC%88a%2Bb%EF%BC%89%26%23178%3B%2B)
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