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计算:(1)(x+y-z)(x+y+z).(2)(x+y-z)(x-y-z).(3)(x+y+z)(x-y-z).(4)(x+y-z)(x-y+z).
题目详情
计算:
(1)(x+y-z)(x+y+z).
(2)(x+y-z)(x-y-z).
(3)(x+y+z)(x-y-z).
(4)(x+y-z)(x-y+z).
(1)(x+y-z)(x+y+z).
(2)(x+y-z)(x-y-z).
(3)(x+y+z)(x-y-z).
(4)(x+y-z)(x-y+z).
▼优质解答
答案和解析
(1)原式=[(x+y)-z][(x+y)+z]
=(x+y)2-z2
=x2+2xy+y2-z2;
(2)原式=[(x-z)+y][(x-z)-y]
=(x-z)2-y2
=x2-2xz+z2-y2;
(3)原式=[x+(y+z)][x-(y+z)]
=x2-(y+z)2
=x2-y2-z2-2yz;
(4)原式=[x+(y-z)][x-(y-z)]
=x2-(y-z)2
=x2-y2-z2+2yz.
=(x+y)2-z2
=x2+2xy+y2-z2;
(2)原式=[(x-z)+y][(x-z)-y]
=(x-z)2-y2
=x2-2xz+z2-y2;
(3)原式=[x+(y+z)][x-(y+z)]
=x2-(y+z)2
=x2-y2-z2-2yz;
(4)原式=[x+(y-z)][x-(y-z)]
=x2-(y-z)2
=x2-y2-z2+2yz.
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