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【种花家务·代数】1-3-07整式的乘方『数理化自学丛书6677版』

2023-09-21 11:25 作者:山嵓  | 我要投稿

【阅前提示】本篇出自『数理化自学丛书6677版』,此版丛书是“数理化自学丛书编委会”于1963-1966年陆续出版,并于1977年正式再版的基础自学教材,本系列丛书共包含17本,层次大致相当于如今的初高中水平,其最大特点就是可用于“自学”。当然由于本书是大半个世纪前的教材,很多概念已经与如今迥异,因此不建议零基础学生直接拿来自学。不过这套丛书却很适合像我这样已接受过基础教育但却很不扎实的学酥重新自修以查漏补缺。另外,黑字是教材原文,彩字是我写的注解。

【山话嵓语】我在原有“自学丛书”系列17册的基础上又添加了1册八五人教中学甲种本《微积分初步》,原因有二:一则,我是双鱼座,有一定程度的偶双症,但“自学丛书”系列中代数4册、几何5册实在令我刺挠,因此就需要加入一本代数,使两边能够对偶平衡;二则,我认为《微积分初步》这本书对“准大学生”很重要,以我的惨痛教训为例,大一高数第一堂课,我是直接蒙圈,学了个寂寞。另外大学物理的前置条件是必须有基础微积分知识,因此我所读院校的大学物理课是推迟开课;而比较生猛的大学则是直接开课,然后在绪论课中猛灌基础高数(例如田光善舒幼生老师的力学课)。我选择在“自学丛书”17本的基础上添加这本《微积分初步》,就是希望小伙伴升大学前可以看看,不至于像我当年那样被高数打了个措手不及。

第三章整式   

§3-7整式的乘方

1、幂的乘方

【01】我们来计算 a⁴·a⁴·a⁴  。这是同底数的幂的乘法。应用§3-6里讲过的同底数的幂的乘法法则,容易算出 a⁴·a⁴·a⁴=a⁴⁺⁴⁺⁴=a⁴*³=a¹²  。

【02】但是,在积 a⁴·a⁴·a⁴ 里,它的三个因式都是 a⁴,所以,这个积的意思就是要计算出幂的三次方的结果,我们可以把它写成以 a⁴ 为底的幂的形式,就是 (a⁴)³  。

【03】我们把这种求一个幂的几次方的计算,叫做幂的乘方。

【04】现在我们再来计算 (a⁵)⁶  。根据乘方的意义,并且应用同底数的幂的乘法法则,容易得到 (a⁵)⁶=a⁵·a⁵·a⁵·a⁵·a⁵·a⁵=a⁵⁺⁵⁺⁵⁺⁵⁺⁵⁺⁵=a⁵*⁶=a³º  。

【05】同样可得 (a²)⁴=a²·a²·a²·a²=a²⁺²⁺²⁺²=a²*4=a⁸  。

【06】一般地说,如果 m 和 n 都是自然数,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】这样我们就得到幂的乘方法则:一个幂乘方,底数不变,把这个幂的指数乘以乘方的指数。即(aᵐ)ⁿ=aᵐⁿ(m,n都是自然数)  。

例1.化简:

%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】必须弄清同底数的幂的乘法与幂的乘方的区别。

a²·a³ 是同底数的幂相乘,a²·a³=a²⁺³=a⁵(指数相加)。

(a²)³ 是幂的乘方,(a²)³=a²*³=a⁶(指数相乘)。

aᵐ·aⁿ 是同底数的幂相乘,aᵐ*ⁿ=aᵐ⁺ⁿ(指数相加)。

(aᵐ)ⁿ 是幂的乘方,(aᵐ)ⁿ=aᵐⁿ(指数相乘)。

习题3-7(1)

计算下列各题:

%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、积的乘方

【08】让我们来计算:(ab)³  。

【09】这里 ab 是两数的积,我们要求的是这积 ab 的三次方。我们把这类计算叫做积的乘方。

【10】根据乘方的意义,得 (ab)³=(ab)(ab)(ab)  。

【11】再根据乘法交换律与结合律,得 (ab)(ab)(ab)=ab·ab·ab=a·a·a·b·b·b=a³b³  。∴ (ab)³=a³b³  。

【12】同样,(xyz)⁵=(xyz)(xyz)(xyz)(xyz)(xyz)=xxxxx·yyyyy·zzzzz=x⁵y⁵z⁵  。

【13】一般地就有积的乘方法则:一个积的乘方,先把各个因式分别乘方,再把所得的结果相乘。即 (ab)ⁿ=mⁿ·bⁿ(n是自然数)。

例2.计算:

%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】积的各因式中如果有数字的因数,计算结果中要把它的乘方的结果算出来,特别要注意负数的乘方法则,不要搞错符号。

【注意2】在第(4)和第(5)小题中,要把-ab 看做是三个因式-1,a,b 的积。

【注意3】第(6)小题中,符号“-”在括号的外边,所以只要先计算出 (ab)⁸ 的结果,再在前面加上“-”号  。

例3.计算:(2x²y²z)⁴  。

【解】(2x²y³z)⁴=2⁴·(x²)⁴·(y³)⁴·z⁴=16x⁸y¹²z⁴  。

【注意】这里积的系数 2 和积中因式 x² 的指数 2,在乘方以后的情况是不同的。2⁴=2×2×2×2=16  。(x²)⁴=x²*⁴=x⁸  。

例4.计算:(1) (x²y³z)ᵐ,(2) (xᵐyᵐ⁺¹z²ᵐ)ⁿ  。

【解】

(1) (x²y³z)ᵐ=(x²)ᵐ(y³)ᵐzᵐ=x²ᵐy³ᵐzᵐ  。

(2) (xᵐyᵐ⁺¹z²ᵐ)ⁿ=(xᵐ)ⁿ(yᵐ⁺¹)ⁿ(z²ᵐ)ⁿ=xᵐⁿy⁽ᵐ⁺¹⁾ⁿ(z²ᵐ)ⁿ=xᵐⁿyᵐⁿ⁺ⁿz2ᵐⁿ  。

【注】在计算熟练以后,也可以省去中间步骤,直接写出结果。例如 (x²y³z)ᵐ=x²ᵐy³ᵐzᵐ  。

例5.计算:(-ab)³(-a²b⁸c)²  。

【解】(-ab)³(-a²b⁸c)²=(-a³b³)(a⁴b⁸c²)=-a⁷b¹¹c²  。

【注意】在第一个括号中,(-1)³→-1,第二个括号中(-1)²=+1  。

习题3-7(2)

计算:

%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、多项式的乘方

【14】多项式的乘方,可以根据乘方的意义,改做多项式的乘法来进行计算。

例6.计算:(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.计算:(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.计算:(x²+3x-1)³  。

【解】用直式演算:

习题3-7(3)

计算(用直式或横式都可以):

%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

【种花家务·代数】1-3-07整式的乘方『数理化自学丛书6677版』的评论 (共 条)

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