{"id":2114,"date":"2024-07-19T19:13:50","date_gmt":"2024-07-19T11:13:50","guid":{"rendered":"http:\/\/zhang.mba\/?p=2114"},"modified":"2024-07-19T19:25:48","modified_gmt":"2024-07-19T11:25:48","slug":"a3-b3-de-gong-shi-tui-dao","status":"publish","type":"post","link":"https:\/\/zhang.mba\/index.php\/2024\/07\/19\/19\/13\/50\/2114\/a3-b3-de-gong-shi-tui-dao\/%e9%ab%98%e7%ad%89%e6%95%b0%e5%ad%a6\/zhangzhiqi\/","title":{"rendered":"$$ a^3 – b^3 $$\u7684\u516c\u5f0f\u63a8\u5bfc"},"content":{"rendered":"

## \u539f\u516c\u5f0f
\n$$ a^3 – b^3 $$<\/p>\n

## \u56e0\u5f0f\u5206\u89e3\u516c\u5f0f
\n$$ a^3 – b^3 = (a – b)(a^2 + ab + b^2) $$<\/p>\n

## \u63a8\u5bfc\u8fc7\u7a0b<\/p>\n

1. \u8003\u8651\u4e24\u4e2a\u6570\u7684\u7acb\u65b9\u5dee\u516c\u5f0f $a^3 – b^3$\u3002
\n2. \u6211\u4eec\u5047\u8bbe $a = b$\uff0c\u90a3\u4e48 $a^3 – b^3 = 0$\uff0c\u8fd9\u8868\u660e $a – b$ \u662f $a^3 – b^3$ \u7684\u4e00\u4e2a\u56e0\u5b50\u3002
\n3. \u4e3a\u4e86\u627e\u5230\u53e6\u4e00\u4e2a\u56e0\u5b50\uff0c\u6211\u4eec\u4f7f\u7528\u591a\u9879\u5f0f\u9664\u6cd5\uff0c\u5c06 $a^3 – b^3$ \u9664\u4ee5 $a – b$\u3002<\/p>\n

### \u591a\u9879\u5f0f\u9664\u6cd5
\n\u6211\u4eec\u5c06 $a^3 – b^3$ \u9664\u4ee5 $a – b$\uff1a<\/p>\n

– \u9996\u5148\uff0c\u6211\u4eec\u8003\u8651 $a^3$ \u9664\u4ee5 $a$ \u5f97\u5230 $a^2$\uff1a
\n $$ \\frac{a^3}{a} = a^2 $$
\n– \u7136\u540e\uff0c\u5c06 $a^2$ \u4e58\u4ee5 $a – b$ \u5f97\u5230 $a^3 – a^2 b$\uff1a
\n $$ a^2 (a – b) = a^3 – a^2 b $$
\n– \u63a5\u7740\uff0c\u7528 $a^3 – b^3$ \u51cf\u53bb $a^3 – a^2 b$ \u5f97\u5230 $a^2 b – b^3$\uff1a
\n $$ (a^3 – b^3) – (a^3 – a^2 b) = a^2 b – b^3 $$<\/p>\n

\u63a5\u4e0b\u6765\uff1a<\/p>\n

– \u8003\u8651 $a^2 b$ \u9664\u4ee5 $a$ \u5f97\u5230 $ab$\uff1a
\n $$ \\frac{a^2 b}{a} = ab $$
\n– \u5c06 $ab$ \u4e58\u4ee5 $a – b$ \u5f97\u5230 $a^2 b – ab^2$\uff1a
\n $$ ab (a – b) = a^2 b – ab^2 $$
\n– \u7528 $a^2 b – b^3$ \u51cf\u53bb $a^2 b – ab^2$ \u5f97\u5230 $ab^2 – b^3$\uff1a
\n $$ (a^2 b – b^3) – (a^2 b – ab^2) = ab^2 – b^3 $$<\/p>\n

\u6700\u540e\uff1a<\/p>\n

– \u8003\u8651 $ab^2$ \u9664\u4ee5 $a$ \u5f97\u5230 $b^2$\uff1a
\n $$ \\frac{ab^2}{a} = b^2 $$
\n– \u5c06 $b^2$ \u4e58\u4ee5 $a – b$ \u5f97\u5230 $ab^2 – b^3$\uff1a
\n $$ b^2 (a – b) = ab^2 – b^3 $$
\n– \u7528 $ab^2 – b^3$ \u51cf\u53bb $ab^2 – b^3$ \u5f97\u5230 0\uff1a
\n $$ (ab^2 – b^3) – (ab^2 – b^3) = 0 $$<\/p>\n

### \u5408\u5e76\u7ed3\u679c
\n\u901a\u8fc7\u591a\u9879\u5f0f\u9664\u6cd5\uff0c\u6211\u4eec\u5f97\u5230\u4e86\uff1a
\n$$ a^3 – b^3 = (a – b)(a^2 + ab + b^2) $$<\/p>\n

## \u6700\u7ec8\u7ed3\u679c
\n\u56e0\u6b64\uff0c$a^3 – b^3$ \u7684\u56e0\u5f0f\u5206\u89e3\u516c\u5f0f\u4e3a\uff1a
\n$$ a^3 – b^3 = (a – b)(a^2 + ab + b^2) $$<\/p>\n\n

<\/div>","protected":false},"excerpt":{"rendered":"

## \u539f\u516c\u5f0f $$ a^3 – b^3 $$ ## \u56e0\u5f0f\u5206\u89e3\u516c\u5f0f $$ a^3 – b^3 = (a – b)(a^2 + ab + b^2) $$ ## \u63a8\u5bfc\u8fc7\u7a0b 1. \u8003\u8651\u4e24\u4e2a\u6570\u7684\u7acb\u65b9\u5dee\u516c\u5f0f $a^3 – b^3$\u3002 2. \u6211\u4eec\u5047\u8bbe $a = b$\uff0c\u90a3\u4e48 $a^3 – b^3 = 0$\uff0c\u8fd9\u8868\u660e $a – b$ \u662f $a^3 – b^3$ \u7684\u4e00\u4e2a\u56e0\u5b50\u3002 3. \u4e3a\u4e86\u627e\u5230 …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0},"categories":[20],"tags":[59],"_links":{"self":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/posts\/2114"}],"collection":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/comments?post=2114"}],"version-history":[{"count":0,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/posts\/2114\/revisions"}],"wp:attachment":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/media?parent=2114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/categories?post=2114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/tags?post=2114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}