25×25 35×35 类似计算的速算技巧，我记得好像有个公式ab×ab=(*+1)(b×b) 记 “*”是新规定的这样一种运算法则：a*b=a2+2ab，比如...

\u4e24\u5411\u91cfA(a,c)\u548cB(b,d)\u7684\u5750\u6807\u76f8\u4e58\u516c\u5f0fA\u00d7B\uff1dab+cd,\u77e5\u9053\u8fd9\u4e2a\u516c\u5f0f\uff0c\u4f46\u4e0d\u77e5\u9053\u6b64\u516c\u5f0f\u662f\u600e

\u8bc1\u660e\uff1a
\u8bbe\u4e24\u4e2a\u5411\u91cfa=OA−\u2192−=(x1,y1),b=OB−\u2192−=(x2,y2)a=OA\u2192=(x1,y1),b=OB\u2192=(x2,y2)\uff0c\u4e24\u5411\u91cf\u5939\u89d2\u4e3a\u03b8\u03b8\uff0c\u5411\u91cf\u70b9\u79ef\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a
a⋅b=|a|⋅|b|cos\u03b8=x1x2+y1y2a⋅b=|a|⋅|b|cos⁡\u03b8=x1x2+y1y2
\u7b2c\u4e00\u90e8\u5206\u53ef\u4ee5\u901a\u8fc7\u89e3\u6790\u51e0\u4f55\u7406\u89e3\uff0c\u5373\u4e00\u4e2a\u5411\u91cf\u5411\u53e6\u4e00\u4e2a\u5411\u91cf\u505a\u6295\u5f71\u3002\u7136\u800c\u7b2c\u4e8c\u90e8\u5206\u7684\u5b9a\u4e49\u6709\u4ec0\u4e48\u610f\u4e49\uff1f\u5173\u952e\u95ee\u9898\u662f\uff0c\u4e3a\u4ec0\u4e48|a|⋅|b|cos\u03b8=x1x2+y1y2|a|⋅|b|cos⁡\u03b8=x1x2+y1y2\uff1f\u4e0b\u9762\u5c31\u5bf9\u8fd9\u4e2a\u95ee\u9898\u8fdb\u884c\u8bc1\u660e\u3002
\u2235OA−\u2192−\u2234BA−\u2192−=OB−\u2192−+BA−\u2192−=OA−\u2192−−OB−\u2192−=(x1−x2,y1−y2)(1)(2)(1)\u2235OA\u2192=OB\u2192+BA\u2192(2)\u2234BA\u2192=OA\u2192−OB\u2192=(x1−x2,y1−y2)
\u5728\u25b3OAB\u25b3OAB\u4e2d\uff0c\u6839\u636e\u4f59\u5f26\u5b9a\u7406\uff1a|BA−\u2192−|2=|OA−\u2192−|2+|OB−\u2192−|2−2|OA−\u2192−||OB−\u2192−|cos\u03b8|BA\u2192|2=|OA\u2192|2+|OB\u2192|2−2|OA\u2192||OB\u2192|cos⁡\u03b8\uff0c\u5e76\u4e14|BA−\u2192−|2=(x1−x2)2+(y1−y2)2|BA\u2192|2=(x1−x2)2+(y1−y2)2\uff0c|OA−\u2192−|2=x21+y21|OA\u2192|2=x12+y12\uff0c|OB−\u2192−|2=x22+y22|OB\u2192|2=x22+y22\uff0c\u6240\u4ee5(x1−x2)2+(y1−y2)2=(x21+y21)+(x22+y22)−2|OA−\u2192−||OB−\u2192−|cos\u03b8(x1−x2)2+(y1−y2)2=(x12+y12)+(x22+y22)−2|OA\u2192||OB\u2192|cos⁡\u03b8\uff0c\u56e0\u6b64\u4fbf\u6709\uff1a
|OA−\u2192−||OB−\u2192−|cos\u03b8=x1x2+y1y2|OA\u2192||OB\u2192|cos⁡\u03b8=x1x2+y1y2
\u5373\uff1a|a|⋅|b|cos\u03b8=x1x2+y1y2
\u53c2\u8003\u8d44\u6599
\u672a\u77e5\uff1ahttp://mail.smhs.kh.edu.tw/~tch044/vector/sub-2.htm

\uff081\uff09\u6839\u636e\u9898\u610f\u5f97\uff1a2*\uff08-3\uff09=4-12=-8\uff1b\uff082\uff09\u6839\u636e\u9898\u610f\u5f97\uff1a2*x=4+4x=2\uff0c\u89e3\u5f97\uff1ax=-12\uff1b\uff083\uff09\u6839\u636e\u9898\u610f\u5f97\uff1a1*x=1+2x\uff0c\u2234\uff08-2\uff09*\uff081*x\uff09=\uff08-2\uff09*\uff081+2x\uff09=4-4\uff081+2x\uff09=x+9\uff0c\u89e3\u5f97\uff1ax=-1\uff0e

25×25
=（2×3）25
=625

35×35
=（3×4）25
=1225

扩展阅读：4x70+1x35铝电缆一米多重 ... 30 60 90特殊三角函数 ... 电缆出铜率对照表 ... 15x15 25x25找规律 ... 15x15 25x25 35x35的规律 ... 万能计算器 ... 4 70+1 35电缆外径 ... 11x11至25x25快速算法 ... 勾股定理30.60.90 ...