【種花家務(wù)·代數(shù)】1-3-07整式的乘方『數(shù)理化自學(xué)叢書(shū)6677版』

2023-09-21 11:25 作者:山嵓 0人讀過(guò) | 我要投稿

【閱前提示】本篇出自『數(shù)理化自學(xué)叢書(shū)6677版』，此版叢書(shū)是“數(shù)理化自學(xué)叢書(shū)編委會(huì)”于1963-1966年陸續(xù)出版，并于1977年正式再版的基礎(chǔ)自學(xué)教材，本系列叢書(shū)共包含17本，層次大致相當(dāng)于如今的初高中水平，其最大特點(diǎn)就是可用于“自學(xué)”。當(dāng)然由于本書(shū)是大半個(gè)世紀(jì)前的教材，很多概念已經(jīng)與如今迥異，因此不建議零基礎(chǔ)學(xué)生直接拿來(lái)自學(xué)。不過(guò)這套叢書(shū)卻很適合像我這樣已接受過(guò)基礎(chǔ)教育但卻很不扎實(shí)的學(xué)酥重新自修以查漏補(bǔ)缺。另外，黑字是教材原文，彩字是我寫(xiě)的注解。

【山話嵓語(yǔ)】我在原有“自學(xué)叢書(shū)”系列17冊(cè)的基礎(chǔ)上又添加了1冊(cè)八五人教中學(xué)甲種本《微積分初步》，原因有二：一則，我是雙魚(yú)座，有一定程度的偶雙癥，但“自學(xué)叢書(shū)”系列中代數(shù)4冊(cè)、幾何5冊(cè)實(shí)在令我刺撓，因此就需要加入一本代數(shù)，使兩邊能夠?qū)ε计胶?；二則，我認(rèn)為《微積分初步》這本書(shū)對(duì)“準(zhǔn)大學(xué)生”很重要，以我的慘痛教訓(xùn)為例，大一高數(shù)第一堂課，我是直接蒙圈，學(xué)了個(gè)寂寞。另外大學(xué)物理的前置條件是必須有基礎(chǔ)微積分知識(shí)，因此我所讀院校的大學(xué)物理課是推遲開(kāi)課；而比較生猛的大學(xué)則是直接開(kāi)課，然后在緒論課中猛灌基礎(chǔ)高數(shù)（例如田光善舒幼生老師的力學(xué)課）。我選擇在“自學(xué)叢書(shū)”17本的基礎(chǔ)上添加這本《微積分初步》，就是希望小伙伴升大學(xué)前可以看看，不至于像我當(dāng)年那樣被高數(shù)打了個(gè)措手不及。

第三章整式? ?

§3-7整式的乘方

1、冪的乘方

【01】我們來(lái)計(jì)算 a?·a?·a?? 。這是同底數(shù)的冪的乘法。應(yīng)用§3-6里講過(guò)的同底數(shù)的冪的乘法法則，容易算出 a?·a?·a?＝a?????＝a?*3＝a12? 。

【02】但是，在積?a?·a?·a? 里，它的三個(gè)因式都是 a?，所以，這個(gè)積的意思就是要計(jì)算出冪的三次方的結(jié)果，我們可以把它寫(xiě)成以 a? 為底的冪的形式，就是 (a?)3? 。

【03】我們把這種求一個(gè)冪的幾次方的計(jì)算，叫做冪的乘方。

【04】現(xiàn)在我們?cè)賮?lái)計(jì)算 (a?)?? 。根據(jù)乘方的意義，并且應(yīng)用同底數(shù)的冪的乘法法則，容易得到 (a?)?＝a?·a?·a?·a?·a?·a?＝a???????????＝a?*?＝a3o? 。

【05】同樣可得 (a2)?＝a2·a2·a2·a2＝a2?2?2?2＝a2*4＝a?? 。

【06】一般地說(shuō)，如果 m 和 n 都是自然數(shù)，那末 $%5Csmall(a%5Em)%5En%3D%5Cunderbrace%7Ba%5Em%5Ccdot%20a%5Em%5Ccdot%5Ccdot%5Ccdot%20a%5Em%7D_%7Bn%5Ctext%7B%20%E4%B8%AA%7D%7D%20%3D%20%5Coverbrace%20%7B%20a%20%5E%20%7B%20m%20%2B%20m%20%2B%20%5Ccdot%20%5Ccdot%20%2B%20m%20%7D%7D%5E%7Bn%5Ctext%7B%20%E4%B8%AA%7D%7D%20%3D%20a%20%5E%20%7Bm%20%5Ccdot%20n%20%7D%20%20$ ? 。

【07】這樣我們就得到冪的乘方法則：一個(gè)冪乘方，底數(shù)不變，把這個(gè)冪的指數(shù)乘以乘方的指數(shù)。即(a?)?＝a??（m，n都是自然數(shù)）? 。

例1.化簡(jiǎn)：

$%5Cscriptsize%5Cbegin%7Baligned%7D%26%5Cbegin%7Barray%7D%7Bccccccc%7D(1)%26(a%5E2)%5E3%3B%26(2)%26(a%5E3)%5E3%3B%26(3)%26(a%5E4)%5E2%3B%26(4)%26(b%5E5)%5E2%3B%5C%5C(5)%26(x%5E%7B12%7D)%5E3%3B%26(6)%26(b%5E7)%5E3%3B%26(7)%26(a%5E%7B2m%7D)%5En%3B%26(8)%26(a%5E%7Bm%2B1%7D)%5En%3B%5C%5C(9)%26(a%5E%7Bm%2B1%7D)%5E%7Bm%2B1%7D%3B%26(10)%26(x%5E%7Bm%2Bn%7D)%5Em.%5Cend%7Barray%7D%5Cend%7Baligned%7D$

【解】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26(1)%5Cquad(a%5E2)%5E3%3Da%5E%7B2%5Ccdot3%7D%3Da%5E6%3B%5C%5C%0A%26%26(2)%5Cquad(a%5E3)%5E3%3Da%5E%7B3%5Ccdot3%7D%3Da%5E9%3B%5C%5C%0A%26%26(3)%5Cquad(a%5E4)%5E3%3Da%5E%7B4%5Ccdot2%7D%3Da%5E8%3B%5C%5C%0A%26%26(4)%5Cquad(b%5E5)%5E2%3Db%5E%7B5%5Ccdot2%7D%3Db%5E%7B19%7D%3B%5C%5C%0A%26%26(5)%5Cquad(x%5E%7B12%7D)%5E3%3Dx%5E%7B12%5Ccdot3%7D%3Dx%5E%7B36%7D%3B%5C%5C%0A%26%26(6)%5Cquad(b%5E7)%5E3%3Db%5E%7B7%5Ccdot3%7D%3Db%5E%7B21%7D%3B%5C%5C%0A%26%26(7)%20%5Cquad(a%5E%7B2m%7D)%5En%3Da%5E%7B2m%5Ccdot%20n%7D%3Da%5E%7B2mn%7D%3B%20%20%5C%5C%0A%26%26(8)%5Cquad%20(a%5E%7Bm%2B1%7D)%5Em%3Da%5E%7B(m%2B1)m%7D%3Da%5E%7Bm%5E2%2Bm%7D%3B%20%20%5C%5C%0A%26%26(9)%20%5Cquad(a%5E%7Bm%2B1%7D)%5E%7Bm%2B1%7D%3Da%5E%7B(m%2B1)(m%2B1)%7D%3Da%5E%7Bm%5E%7B2%7D%2B2m%2B1%7D%3B%20%20%5C%5C%0A%26%26(10)%5Cquad%20(a%5E%7Bm%2Bn%7D)%5Em%3Da%5E%7B(m%2Bn)m%7D%3Da%5E%7Bm%5E2%2Bmn%7D.%20%0A%5Cend%7Beqnarray%7D$

【注意】必須弄清同底數(shù)的冪的乘法與冪的乘方的區(qū)別。

a2·a3 是同底數(shù)的冪相乘，a2·a3＝a2?3＝a?（指數(shù)相加）。

(a2)3 是冪的乘方，(a2)3＝a2*3＝a?（指數(shù)相乘）。

a?·a? 是同底數(shù)的冪相乘，a?*?＝a???（指數(shù)相加）。

(a?)? 是冪的乘方，(a?)?＝a??（指數(shù)相乘）。

習(xí)題3-7(1)

計(jì)算下列各題：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%261%E3%80%81(x%5E%7B2%7D)%5E%7B2%7D.%26%262%E3%80%81(a%5E2)%5E3%26%26%203%E3%80%81x%5E%7B2%7D%5Ccdot%20x%5E%7B2%7D.%20%20%5C%5C%0A%26%264%E3%80%81a%5E2%5Ccdot%20a%5E4.%26%26%205%E3%80%81(a%5E%7B12%7D)%5E%7B3%7D%20%26%26%206%E3%80%81a%5E%7B12%7D%5Ccdot%20a%5E%7B3%7D.%20%20%5C%5C%0A%26%267%E3%80%81(b%5E%7B3%7D)%5E%7B4%7D.%26%26%208%E3%80%81b%5E%7B3%7D%5Ccdot%20b%5E%7B4%7D.%20%26%26%209%E3%80%81(y%5E%7B5%7D)%5E%7B5%7D.%20%20%5C%5C%0A%26%2610%E3%80%81y%5E%7B5%7D%5Ccdot%20y%5E%7B5%7D.%26%26%2011%E3%80%81(a%5E%7B2m%7D)%5E%7Bn%7D.%20%26%26%2012%E3%80%81a%5E%7B2m%7D%5Ccdot%20a%5En.%20%20%5C%5C%0A%26%2613%E3%80%81a%5E%7Bm%7D%5Ccdot%20a%5E%7B2%7D.%26%26%2014%E3%80%81(a%5E%7Bm%7D)%5E%7B2%7D.%20%26%26%2015%E3%80%81(a%5E%7B16%7D)%5E%7B20%7D.%20%20%5C%5C%0A%26%2616%E3%80%81a%5E%7B16%7D%5Ccdot%20a%5E%7B20%7D%20%20%26%26%2017%E3%80%81%5B(a%5E%7B3%7D)%5E%7B2%7D%5D%5E%7B4%7D.%20%26%26%2018%E3%80%81a%5E%7B3%7D%5Ccdot%20a%5E%7B2%7D%5Ccdot%20a%5E%7B4%7D.%20%20%5C%5C%0A%26%2619%E3%80%81%5Cleft%5B(a%5E%7Bm%7D)%5E%7Bn%7D%5Cright%5D%5E%7Bp%7D.%20%26%26%2020%E3%80%81a%5E%7B%5Cboldsymbol%7Bm%7D%5Ccdot%20a%5E%7Bn%7D%5Ccdot%20a%5E%7Bp%7D%7D.%20%26%26%2021%E3%80%81(a%5E%7B2%7D)%5E%7B3%7D%5Ccdot(a%5E%7B5%7D)%5E%7B2%7D.%20%20%5C%5C%0A%26%2622%E3%80%81(a%5E%7B3%7D)%5E%7B4%7D%5Ccdot(a%5E%7B2%7D)%5E%7B4%7D.%26%26%2023%E3%80%81(a%5E%7B%5Cboldsymbol%7Bm%7D%7D)%5E%7B2%7D%5Ccdot(a%5E%7Bn%7D)%5E%7B3%7D.%20%26%2624%E3%80%81(x%5E2)%5Em%5Ccdot(x%5E3)%5En.%20%20%5C%5C%0A%26%2625%E3%80%81(a%5E%7B2%7D)%5E%7B3%7D%5Ccdot%20a%5E%7B5%7D.%20%26%26%2026%E3%80%81(a%5E%7B2%7D%C2%B7a%5E%7B3%7D)%5E%7B5%7D.%20%26%26%2027%E3%80%81a%5E%7B2%7D%C2%B7a%5E%7B3%7D%2Ba%5E%7B5%7D%E3%80%82%20%20%5C%5C%0A%26%2628%E3%80%81(a%5E%7B2%7D)%5E%7B3%7D%2B(a%5E%7B3%7D)%5E%7B2%7D.%20%26%26%2029%E3%80%81a%5E%7B2%7D)%5E%7B3%7D%2Ba%5E%7B5%7D.%20%26%26%2030%E3%80%81a%5E%7B2%7D%5Ccdot%20a%5E%7B3%7D%2Ba%5E%7B6%7D.%20%0A%5Cend%7Beqnarray%7D$

【答案】

$%5Cscriptsize%5Cbegin%7Baligned%7D%0A%5Cbegin%7Barray%7D%7Bcccccccccc%7D%0A1.%26%20x%5E4%3B%262%26a%5E6%3B%263.%26%20x%5E4%3B%264.%26%20a%5E6%3B%265.%26%20a%5E%7B56%7D%3B%5C%5C%0A6.%26a%5E%7B15%7D%3B%267.%26b%5E%7B12%7D%3B%268.%26b%5E7%3B%269.%26y%5E%7B25%7D%3B%2610.%26y%5E%7B10%7D%3B%5C%5C%0A11.%26a%5E%7B2%5Cpi%20nn%7D%3B%2612.%26a%5E%7B2m%2Bn%7D%3B%2613.%26a%5E%7Bm%2B2%7D%3B%2614.%26a%5E%7B2m%7D%3B%2615.%26a%5E%7B376%7D%3B%5C%5C%0A16.%26a%5E%7B36%7D%3B%2617.%26a%5E%7B24%7D%3B%2618.%26a%5E9%3B%2619.%26a%5E%7Bmnp%7D%3B%2620.%26a%5E%7Bm%2Bn%2Bp%7D%3B%5C%5C%0A21.%26a%5E%7B16%7D%3B%2622.%26a%5E%7B20%7D%3B%2623.%26a%5E%7B2m%2B3n%7D%3B%2624.%26x%5E%7B2m%2B3n%7D%3B%2625.%26a%5E%7B11%7D%3B%5C%5C%0A26.%26a%5E%7B25%7D%3B%2627.%262a%5E%7B5%7D%3B%2628.%262c%5E6%3B%2629.%26a%5E6%2Ba%5E5%3B%2630.%26a%5E5%2Ba%5E6.%5Cend%7Barray%7D%5Cend%7Baligned%7D$

2、積的乘方

【08】讓我們來(lái)計(jì)算：(ab)3? 。

【09】這里 ab 是兩數(shù)的積，我們要求的是這積 ab 的三次方。我們把這類計(jì)算叫做積的乘方。

【10】根據(jù)乘方的意義，得 (ab)3＝(ab)(ab)(ab)? 。

【11】再根據(jù)乘法交換律與結(jié)合律，得 (ab)(ab)(ab)＝ab·ab·ab＝a·a·a·b·b·b＝a3b3? 。∴ (ab)3＝a3b3? 。

【12】同樣，(xyz)?＝(xyz)(xyz)(xyz)(xyz)(xyz)＝xxxxx·yyyyy·zzzzz＝x?y?z?? 。

【13】一般地就有積的乘方法則：一個(gè)積的乘方，先把各個(gè)因式分別乘方，再把所得的結(jié)果相乘。即 (ab)?＝m?·b?（n是自然數(shù)）。

例2.計(jì)算：

$%5Cscriptsize%5Cbegin%7Barray%7D%7Bcccccc%7D(1)%26(2ab)%5E3%3B%26(2)%26(-3ab)%5E2%3B%26(3)%26(-2xyz)%5E3%3B%5C%5C(4)%26(-ab)%5E5%3B%26(5)%26(-ab)%5E8%3B%26(6)%26-(ab)%5E8.%5Cend%7Barray%7D$

【解】

$%5Cscriptsize%5Cbegin%7Baligned%7D%0A%26(1)(2ab)%5E3%3D2%5E3a%5E3b%5E3%3D8a%5E3b%5E3%3B%20%5C%5C%0A%26(2)(-3ab)%5E2%3D(-3)%5E2a%5E2b%5E2%3D9a%5E2b%5E2%3B%20%5C%5C%0A%26(3)(-2xyz)%5E3%3D(-2)%5E3x%5E3y%5E3z%5E3%3D-8x%5E3y%5E3z%5E3%3B%20%5C%5C%0A%26(4)(-ab)%5E5%3D(-1)%5E5a%5E5b%5E5%3D-a%5E5b%5E5%3B%20%5C%5C%0A%26(5)(-ab)%5E%7B8%7D%3D(-1)%5E%7B8%7Da%5E%7B8%7Db%5E%7B8%7D%3Da%5E%7B8%7Db%5E%7B8%7D%3B%20%5C%5C%0A%26(6)-(ab)%5E8%3D-a%5E8b%5E8.%0A%5Cend%7Baligned%7D$

【注意1】積的各因式中如果有數(shù)字的因數(shù)，計(jì)算結(jié)果中要把它的乘方的結(jié)果算出來(lái)，特別要注意負(fù)數(shù)的乘方法則，不要搞錯(cuò)符號(hào)。

【注意2】在第(4)和第(5)小題中，要把－ab 看做是三個(gè)因式－1，a，b 的積。

【注意3】第(6)小題中，符號(hào)“－”在括號(hào)的外邊，所以只要先計(jì)算出 (ab)? 的結(jié)果，再在前面加上“－”號(hào)? 。

例3.計(jì)算：(2x2y2z)?? 。

【解】(2x2y3z)?＝2?·(x2)?·(y3)?·z?＝16x?y12z?? 。

【注意】這里積的系數(shù) 2 和積中因式 x2 的指數(shù) 2，在乘方以后的情況是不同的。2?＝2×2×2×2＝16? 。(x2)?＝x2*?＝x?? 。

例4.計(jì)算：(1) (x2y3z)?，(2) (x?y??1z2?)?? 。

【解】

(1)?(x2y3z)?＝(x2)?(y3)?z?＝x2?y3?z?? 。

(2) (x?y??1z2?)?＝(x?)?(y??1)?(z2?)?＝x??y???1??(z2?)?＝x??y????z2??? 。

【注】在計(jì)算熟練以后，也可以省去中間步驟，直接寫(xiě)出結(jié)果。例如 (x2y3z)?＝x2?y3?z?? 。

例5.計(jì)算：(－ab)3(－a2b?c)2? 。

【解】(－ab)3(－a2b?c)2＝(－a3b3)(a?b?c2)＝－a?b11c2? 。

【注意】在第一個(gè)括號(hào)中，(－1)3→－1，第二個(gè)括號(hào)中(－1)2＝＋1? 。

習(xí)題3-7(2)

計(jì)算：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%261%E3%80%81(3a%5E2b%5E3)%5E4.%5C%5C%0A%26%262%E3%80%81(-2a%5E%7B5%7Db%5E%7B3%7Dc)%5E%7B4%7D.%20%20%5C%5C%0A%26%263%E3%80%81(-ab%5E%7B2%7Dc%5E%7B3%7D)%5E%7B101%7D.%5C%5C%0A%26%264%E3%80%81%5Cleft(%5Cfrac%7B1%7D%7B2%7Dx%5E%7B2%7Dy%5Cright)%5E%7B3%7D.%20%20%5C%5C%26%26%0A5%E3%80%81%5Cleft(-%5Cfrac%7B2%7D%7B3%7Da%5E%7B3%7Dbc%5E%7B2%7D%5Cright)%5E%7B3%7D.%5C%5C%0A%26%26%0A6%E3%80%81%5Cleft(1%5Cfrac%7B1%7D%7B2%7Da%5E%7B2%7Dx%5Cright)%5E%7B4%7D.%20%20%5C%5C%0A%26%26%0A7%E3%80%81(0.3a%5E2)%5E3.%5C%5C%0A%26%26%0A%208%E3%80%81(3a%5E%7B2%7Db%5E%7B3%7Dxy)%5E%7B4%7D%E3%80%82%20%5C%5C%0A%26%26%0A9%E3%80%81(2a%5E2b%5E4xy%5E3)%5E2.%5C%5C%0A%26%26%0A10%E3%80%81(x%5E2y)%5Em.%5C%5C%0A%26%26%0A11%E3%80%81(x%5Emy)%5E2.%5C%5C%0A%26%26%0A12%E3%80%81(x%5Emy%5En)%5E2.%5C%5C%0A%26%26%0A13%E3%80%81(x%5Emy)%5En.%5C%5C%0A%26%26%0A14%E3%80%81(2a%5E2)%5E3%5Ccdot(3a%5E9)%5E2.%5C%5C%0A%26%26%0A15%E3%80%81(x%5E2y%5E3)%5E5%5Ccdot(xy%5E2)%5E4.%5C%5C%0A%26%26%0A16%E3%80%81(-a%5E3b%5E2)%5E5%5Ccdot(a%5E2b%5E3)%5E6.%5C%5C%0A%26%26%0A17%E3%80%81%5Cleft(%5Cfrac%7B1%7D%7B2%7Da%5E%7B3%7D%5Cright)%5E%7B2%7D%5Ccdot(-2a%5E%7B2%7D)%5E%7B3%7D.%5C%5C%0A%26%26%0A18%E3%80%81(-a%5E%7B3%7Db%5E%7B5%7D)%5E%7B4%7D%5Ccdot(-a%5E%7B2%7Dc)%5E%7B3%7D.%20%5C%5C%0A%26%26%0A19%E3%80%813a%5E%7B2%7Db%5E%7B3%7D(3ab%5E%7B2%7D)%5E%7B3%7D%5Ccdot(2a%5E%7B2%7Db)%5E%7B2%7D.%5C%5C%0A%26%26%0A20%E3%80%81(a%5E%7Bn%7Db%5E%7Bn%7Dc)%5E%7B3%7D%5Ccdot(a%5E%7Bn%7Db%5E%7Bm%7Dc%5E%7Bm%7D)%5E%7B2%7D.%20%20%5C%5C%0A%26%26%0A21%E3%80%81(3a%5E3)%5E2%2Ba%5E6.%5C%5C%0A%26%26%0A22%E3%80%81(3a%5E3)%5E3%2Ba%5E9.%5C%5C%0A%26%26%0A23%E3%80%81(a%5E6)%5E6%2Ba%5E6%5Ccdot%20a%5E6.%5C%5C%0A%26%26%0A24%E3%80%81(-5a%5E5)%5E2%2B(3a%5E3)%5E3%0A%5Cend%7Beqnarray%7D$

【答案】

$%5Cscriptsize%5Cbegin%7Baligned%7D%5Cbegin%7Barray%7D%7Bccccccccc%7D1.%26%5Cquad81a%5E%7B9%7Db%5E%7B12%7D%3B%262.%26%5Cquad16a%5E%7B20%7Db%5E%7B12%7Dc%5E%7B4%7D%3B%263.%26-a%5E%7B101%7Db%5E%7B202%7Dc%5E%7B309%7D%3B%264.%26%5Cfrac18x%5E6y%5E6%3B%5C%5C5.%26-%5Cfrac8%7B27%7Da%5E9b%5E3x%5E6%3B%266.%26%5Cfrac%7B81%7D%7B16%7D%5C%3Aa%5E8x%5E4%3B%267.%260.027a%5E6%3B%268.%2681a%5E%7B81%7Db%5E%7B12%7Dx%5E4y%5E4%3B%5C%5C9.%264a%5E4b%5E8x%5E2y%5E6%3B%2610.%26x%5E%7B2m%7Dy%5E%7Bm%7D%3B%2611.%26x%5E%7B2m%7Dy%5E2%3B%2612.%26x%5E%7B2m%7Dy%5E%7B2n%7D%3B%5C%5C13.%26x%5E%7Bmn%7Dy%5En%3B%2614.%2672a%5E%7B12%7D%3B%2615.%26x%5E%7B14%7Dy%5E%7B24%7D%3B%2616.%26-a%5E%7B27%7Db%5E%7B2k%7D%3B%5C%5C17.%26-2a%5E%7B12%7D%3B%2618.%26-a%5E%7B19%7Db%5E%7B2n%7Dc%5E3%3B%2619.%26324a%5E9b%5E%7B11%7D%3B%2620.%26a%5E%7B8m%2B2m%7Db%5E%7B2m%2B3n%7Dc%5E%7B2m%2B8%7D%3B%5C%5C21.%2610a%5E6%3B%2622.%2628a%5E9%3B%2623.%26%5Ccdot%20a%5E%7B66%7D%2Ba%5E%7B12%7D%3B%2624.%2625a%5E%7B10%7D%2B27a%5E9.%5Cend%7Barray%7D%5Cend%7Baligned%7D$

3、多項(xiàng)式的乘方

【14】多項(xiàng)式的乘方，可以根據(jù)乘方的意義，改做多項(xiàng)式的乘法來(lái)進(jìn)行計(jì)算。

例6.計(jì)算：(a＋b)2? 。

【解】(a＋b)2＝(a＋b)(a＋b)＝a2＋ab＋ab＋b2＝a2＋2ab＋b2? 。

【注意】(a＋b)2不等于a2＋b2? 。

例7.計(jì)算：(a＋b)3? 。

【解】

$%5Cscriptsize%5Cbegin%7Baligned%7D%0A%5Cleft(a%2Bb%5Cright)%5E%7B3%7D%26%20%3D%5Cleft(a%2Bb%5Cright)%5Cleft(a%2Bb%5Cright)%5Cleft(a%2Bb%5Cright)%20%20%5C%5C%0A%26%3D(a%5E2%2Bab%2Bab%2Bb%5E2)(a%2Bb)%20%5C%5C%0A%26%3D%5Cleft(a%5E2%2B2ab%2Bb%5E2%5Cright)%5Cleft(a%2Bb%5Cright)%20%5C%5C%0A%26%3Da%5E3%2B2a%5E2b%2Bab%5E2%2Ba%5E2b%2B2ab%5E2%2Bb%5E3%20%5C%5C%0A%26%3Da%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3.%0A%5Cend%7Baligned%7D$

例8.計(jì)算：(x2＋3x－1)3? 。

【解】用直式演算：

習(xí)題3-7(3)

計(jì)算（用直式或橫式都可以）：

$%5Cscriptsize%5Cbegin%7Baligned%7D%0A%261%E3%80%81(x%2By)%5E%7B2%7D.%26%26%202%E3%80%81(x-y)%5E%7B2%7D.%20%20%5C%5C%0A%263%E3%80%81(a%2B2b)%5E%7B2%7D.%26%26%204%E3%80%81(3a-4b)%5E%7B2%7D.%20%20%5C%5C%0A%265%E3%80%81(x%2By)%5E%7B3%7D.%26%26%206%E3%80%81(x-y)%5E%7B3%7D.%20%20%5C%5C%0A%26%207%E3%80%81(a%2Bb%2Bc)%5E%7B2%7D.%20%26%26%208%E3%80%81(a-b-c)%5E%7B2%7D.%20%20%5C%5C%0A%269%E3%80%81(3x%5E2-3x%2B2)%5E2.%26%26%2010%E3%80%81(a%2Bb)%5E%7B4%7D.%20%0A%5Cend%7Baligned%7D$

標(biāo)簽：

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【種花家務(wù)·代數(shù)】1-3-07整式的乘方『數(shù)理化自學(xué)叢書(shū)6677版』

習(xí)題3-7(1)

習(xí)題3-7(2)

習(xí)題3-7(3)