【種花家務(wù)·代數(shù)】1-3-04整式的加減法『數(shù)理化自學(xué)叢書6677版』

2023-09-18 17:10 作者:山嵓 0人讀過 | 我要投稿

【閱前提示】本篇出自『數(shù)理化自學(xué)叢書6677版』，此版叢書是“數(shù)理化自學(xué)叢書編委會(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)生直接拿來自學(xué)。不過這套叢書卻很適合像我這樣已接受過基礎(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，彩字是我寫的注解。

【山話嵓語】我在原有“自學(xué)叢書”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，我是雙魚座，有一定程度的偶雙癥，但“自學(xué)叢書”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)物理課是推遲開課；而比較生猛的大學(xué)則是直接開課，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”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??

§3-4整式的加減法

1、單項(xiàng)式的加法

【01】應(yīng)用上面所講過的合并同類項(xiàng)的法則，我們很容易做關(guān)于單項(xiàng)式的加法。舉例說明如下：

例1.求下面各題里的這些單項(xiàng)式的和：(1)3a,－5a；(2)3a,－4b,－5a；(3)3a,－4b? 。

【解】

(1) 3a 和－5a 相加，它們的和就是 3a＋(－5a)? 。把它寫成代數(shù)和的形式，再合并同類項(xiàng)，得3a＋(－5a)＝3a－5a＝－2a? 。

(2) 3a＋(－4b)＋(－5a)＝3a－4b－5a＝3a－5a－4b＝－2a－4b? 。

(3) 3a＋(－4b)＝3a－4b? 。

【02】從上面的例子可以看到，做單項(xiàng)式的加法，有下面的單項(xiàng)式的加法法則：幾個(gè)單項(xiàng)式相加，只要把這些單項(xiàng)式連結(jié)起來寫成代數(shù)和的形式，再合并同類項(xiàng)。

【注】把幾個(gè)代數(shù)式相加時(shí)，我們把這些代數(shù)式都叫做加式。

例2.做下面的加法：

$%5Cscriptsize%5Cbegin%7Baligned%7D%26(1)(-3ab)%2B(-2ab)%2B(%2B5ab)%3B%5C%5C%26(2)%5Cleft(-%5Cfrac%7B1%7D%7B2%7Dx%5Cright)%2B%5Cleft(-%5Cfrac%7B1%7D%7B3%7Dx%5Cright)%2B%5Cleft(%2B%5Cfrac%7B1%7D%7B2%7Dx%5Cright)%2B%5Cleft(%2B%5Cfrac%7B1%7D%7B3%7Dx%5E2%5Cright).%5Cend%7Baligned%7D$

【解】

(1) (－3ab)＋(－2ab)＋(＋5ab)＝－3ab－2ab＋5ab＝0? 。

(2)

$%5Cscriptsize%5Cbegin%7Baligned%7D%26%5Cleft(-%5Cfrac%7B1%7D%7B2%7Dx%5Cright)%2B%5Cleft(-%5Cfrac%7B1%7D%7B3%7Dx%5Cright)%2B%5Cleft(%2B%5Cfrac%7B1%7D%7B2%7Dx%5Cright)%2B%5Cleft(%2B%5Cfrac%7B1%7D%7B3%7Dx%5E2%5Cright)%5C%5C%26%3D%5Cunderline%7B-%5Cfrac%7B1%7D%7B2%7Dx%7D-%5Cfrac%7B1%7D%7B3%7Dx%2B%5Cunderline%7B%5Cfrac%7B1%7D%7B2%7Dx%7D%2B%5Cfrac%7B1%7D%7B3%7Dx%5E2%3D-%5Cfrac%7B1%7D%7B3%7Dx%2B%5Cfrac%7B1%7D%7B3%7Dx%5E2%3D%5Cfrac%7B1%7D%7B3%7Dx%5E2-%5Cfrac%7B1%7D%7B3%7Dx.%5Cend%7Baligned%7D$

【注意】

????????在(1)中合并同類項(xiàng)以后 ab 的系數(shù)是 0，所以結(jié)果是 0? 。

????????在(2)中? $%5Cscriptsize-%5Cfrac%7B1%7D%7B3%7D%20x%0A$ 和? $%5Cscriptsize%5Cfrac%7B1%7D%7B3%7D%20x%5E2%0A$ ?不是同類項(xiàng)，所以不能再合并。最后結(jié)果用 x 的降冪排列，這祥可以避免第一項(xiàng)的系發(fā)是負(fù)數(shù)。但是把? $%5Cscriptsize-%5Cfrac%7B1%7D%7B3%7D%20x%2B%5Cfrac%7B1%7D%7B3%7D%20x%5E2%0A$ ?當(dāng)做最后的結(jié)果也是可以的。

習(xí)題3-4(1)

1、做下面的加法：

$%5Cscriptsize%5Cbegin%7Baligned%7D(1)%263a%2B(%2B7a)%3B%26(2)%26(-3a)%2B(-7a)%3B%5C%5C(3)%263x%2B(-7x)%3B%26(4)%26(-3x)%2B(%2B7x)%3B%5C%5C(5)%26%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B1%7D%7B3%7Dx%3B%26(6)%26(-%5Cfrac%7B1%7D%7B3%7Da)%2B%5Cleft(%2B%5Cfrac%7B1%7D%7B2%7Da%5Cright).%5Cend%7Baligned%7D$

2、求下列各式的和：

$%5Cscriptsize%5Cbegin%7Barray%7D%7Bllll%7D%7B(1)%7D%26%7B3x%5E%7B2%7D%2C%5C%3B-5x%5E%7B2%7D%3B%7D%26%7B(2)%7D%7B-3a%5E%7B3%7D%2C%5C%3B-5a%5E%7B3%7D%3B%7D%5C%5C%7B(3)%7D%26%7B-8a%5E%7B2%7Db%5E%7B3%7D%2C%5C%3B%2B9a%5E%7B2%7Db%5E%7B3%7D%3B%7D%26%7B(4)%7D%7Bx%5E%7B2%7Dy%2C%5C%3B-x%5E%7B2%7Dy%3B%7D%5C%5C%7B(5)%7D%26%7B%5Cfrac%7B2%7D%7B3%7Da%5E%7B2%7Dx%5E%7B2%7D%2C%5C%3B-%5Cfrac%7B3%7D%7B4%7Da%5E%7B2%7Dx%5E%7B2%7D%3B%7D%26%7B(6)0.3a%5E%7B2%7Db%5E%7B3%7Dc%2C%5C%3B-%5Cfrac%7B1%7D%7B3%7Da%5E%7B2%7Db%5E%7B3%7Dc.%7D%5Cend%7Barray%7D$

3、計(jì)算：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26(1)(%2B3a)%2B(-5b)%3B%5Cquad%26%26(2)(-5a%5E2)%2B(-5a)%3B%5C%5C%0A%26%26(3)(-3a%5E2b)%2B(-5ab%5E2)%3B%26%26(4)(%2B%5Cfrac12a%5E3b%5E3)%2B(%2B%5Cfrac13a%5E3b%5E2)%3B%5C%5C%0A%26%26(5)(-3a%5E2x%5E3)%2B(-5a%5E2x)%3B%26%26(6)(-3xy)%2B(%2B5ay).%0A%5Cend%7Beqnarray%7D$

4、計(jì)算：

$%5Cscriptsize%5Cbegin%7Baligned%7D%0A%26(1)(%2B3a)%2B(-5a)%2B(-7a)%3B%20%5C%5C%0A%26(2)(-7a%5E%7B2%7D)%2B(%2B5a%5E%7B2%7D)%2B(%2B2a%5E%7B2%7D)%3B%20%5C%5C%0A%26(3)(-7a%5E%7B2%7Db%5E%7B3%7D)%2B(-11a%5E%7B2%7Db%5E%7B3%7D)%2B(-14a%5E%7B3%7Db%5E%7B2%7D)%3B%20%5C%5C%0A%26(4)(-5a%5E2x%5E3)%2B(%2B5a%5E3x%5E2)%2B(-3a%5E3x%5E2)%3B%20%5C%5C%0A%26(5)(%2B7abx%5E%7B2%7D)%2B(-4ab%5E%7B2%7Dx)%2B(-3a%5E%7B2%7Dbx)%3B%5C%5C%0A%26(6)(-3a%5E%7B2%7Dx%5E%7B2%7Dy%5E%7B2%7D)%2B(%2B5a%5E%7B2%7Dx%5E%7B3%7Dy%5E%7B2%7D)%2B(-3a%5E%7B6%7Dx%5E%7B2%7Dy%5E%7B2%7D).%0A%5Cend%7Baligned%7D$

5、計(jì)算：

$%5Cscriptsize%5Cbegin%7Baligned%7D%0A%26%5Ctext%7B(1)%7D%20(%2B3a)%2B(-5a)%2B(-7a)%2B(-31a)%3B%20%20%5C%5C%0A%26%5Ctext%7B(2)%7D%20%5Cleft(%2B%5Cfrac%7B1%7D%7B2%7Dab%5Cright)%2B%5Cleft(-%5Cfrac%7B1%7D%7B3%7Dab%5Cright)%2B%5Cleft(%2B%5Cfrac%7B1%7D%7B4%7Dab%5Cright)%2B%5Cleft(-%5Cfrac%7B1%7D%7B5%7Dab%5Cright)%3B%20%20%5C%5C%0A%26%5Ctext%7B(3)%7D%20%5Cleft(%2B%5Cfrac%7B2%7D%7B3%7Dx%5E%7B2%7Dy%5Cright)%2B%5Cleft(-%5Cfrac%7B3%7D%7B2%7Dx%5E%7B2%7Dy%5Cright)%2B%5Cleft(-%5Cfrac%7B2%7D%7B3%7Dxy%5E%7B2%7D%5Cright)%2B%5Cleft(%2B%5Cfrac%7B1%7D%7B4%7Dxy%5E%7B2%7D%5Cright)%3B%20%20%5C%5C%0A%26%5Ctext%7B(4)%7D%205a%5E%7B3%7Dx%5E%7B2%7D%2B(-3a%5E%7B2%7Dx%5E%7B5%7D)%2B(%2B5a%5E%7B3%7Dx%5E%7B2%7D)%2B(-3a%5E%7B2%7Dx%5E%7B3%7D)%3B%20%20%5C%5C%0A%26%5Ctext%7B(5)%7D%20%5Cleft(-%5Cfrac%7B1%7D%7B2%7Dabx%5E%7B2%7D%5Cright)%2B%5Cleft(-%5Cfrac%7B1%7D%7B3%7Dabx%5Cright)%2B%5Cleft(-%5Cfrac%7B1%7D%7B4%7Dabx%5E%7B2%7D%5Cright)%2B%5Cleft(-%5Cfrac%7B1%7D%7B3%7Dab%5E%7B2%7Dx%5Cright)%3B%20%20%5C%5C%0A%26%5Ctext%7B(6)%7D%20(-2a%5E%7B2%7Db%5E%7B3%7Dxy)%2B(-3a%5E%7B2%7Db%5E%7B3%7Dxy)%2B(-5a%5E%7B3%7Db%5E%7B2%7Dxy)%2B(-6a%5E%7B3%7Db%5E%7B2%7Dxy).%20%0A%5Cend%7Baligned%7D$

【答案】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A4%E3%80%81%26%26(1)%5Cquad-9a%2C%5Cquad(2)%5Cquad0%2C%5Cquad(3)%5Cquad-18a%5E2b%5E3-14a%5E3b%5E3%2C%5C%5C%0A%26%26(4)%5Cquad-5a%5E2x%5E3%2B2a%5E2x%5E2%2C%5Cquad(5)%5Cquad7abx%5E2-4ab%5E2x-3a%5E2bx%2C%5C%5C%0A%26%26(6)%5Cquad-3a%5E2x%5E2y%5E3%2B5a%5E2x%5E3y%5E2-3a%5E3x%5E2y%5E2%3B%5C%5C%0A5%E3%80%81%26%26(1)%5Cquad-40a%2C%5Cquad(2)%5Cquad%5Cfrac%7B13%7D%7B60%7Dab%2C%5C%5C%0A%26%26(3)%5Cquad-%5Cfrac56x%5E2y-%5Cfrac5%7B12%7Dxy%5E2%2C%5Cquad(4)%5Cquad10a%5E3x%5E2-6a%5E2x%5E3%2C%5C%5C%0A%26%26(5)%5Cquad-%5Cfrac34abx%5E2-%5Cfrac13abx-%5Cfrac13ab%5E2x%2C%5Cquad(6)%5Cquad-5a%5E2b%5E3xy-11a%5E3b%5E2xy.%0A%5Cend%7Beqnarray%7D$

2、單項(xiàng)式的減法

【03】在有理數(shù)的減法里，我們知道，減去一個(gè)數(shù)，等于加上它的相反的數(shù)。用字母來表示，就是a－(＋b)＝a＋(－b)，a－(－b)＝a＋(＋b)? 。

【04】所以做單項(xiàng)式的減法，只需應(yīng)用下面的單項(xiàng)式的減法法則：減去一個(gè)單項(xiàng)式，只要把這個(gè)單項(xiàng)式的性質(zhì)符號(hào)改成相反的符號(hào)，再做加法。

【注】一個(gè)代數(shù)式減去另一個(gè)代數(shù)式，我們把第一個(gè)代數(shù)式叫做被減式，第二個(gè)代數(shù)式叫做減式。

例3.做下列減法：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26(1)5a-(%2B3a)%3B%5Cquad%26%26(2)5a-(%2B8a)%3B%5C%5C%0A%26%26(3)(-5a)-(%2B3a)%3B%26%26(4)(-5a)-(-8a)%3B%5C%5C%0A%26%26(5)(-5a%5E3)-(-7a%5E3)%3B%26%26(6)(%2Ba%5E4b%5E3)-(-a%5E2b%5E3).%5C%0A%5Cend%7Beqnarray%7D$

【解】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26%20(1)5a-(%2B3a)-5a%2B(-3a)%3D5a-3a%3D2a%3B%20%20%5C%5C%0A%26%26(2)5a-(%2B8a)%3D5a%2B(-8a)-5a-8a%3D-3a%2C%20%5C%5C%0A%26%26(3)(-5a)-(%2B3a)-(-5a)%2B(-3a)%20%3D-5a-3a%3D-8a%3B%20%5C%5C%0A%26%26(4)(-5a)-(-8a)%20%3D(-5a)%2B(%2B8a)%20%3D-5a%2B8a%3D%2B3a%3B%5C%5C%0A%26%26(5)(-5a%5E3)-(-7a%5E3)%3D(-5a%5E3)%2B(%2B7a%5E3)%3D-5a%5E3%2B7a%5E3%3D2a%5E3%3B%5C%5C%0A%26%26(6)(%2Ba%5E2b%5E3)-(-a%5E2b%5E3)%3Da%5E2b%5E3%2B(%2Ba%5E2b%5E3)%3Da%5E2b%5E3%2Ba%5E2b%5E3%3D2a%5E2b%5E3.%0A%5Cend%7Beqnarray%7D$

例4.計(jì)算：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%26%26(1)3a-(%2B5b)%3B%5Cquad%26%26(2)5a-(-3b)%3B%5C%5C%26%26(3)3a%5E2-(%2B2a)%3B%26%26(4)3a%5E2-(-3a).%0A%5Cend%7Beqnarray%7D$

【解】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26%20(1)3a-(%2B5b)%3D3a%2B(-5b)%3D3a-5b%3B%20%5C%5C%0A%26%26%20(2)5a-(-3b)%3D5a%2B(%2B3b)%3D5a%2B3b%3B%20%5C%5C%0A%26%26%20(3)3a%5E%7B2%7D-(%2B2a)-3a%5E%7B2%7D%2B(-2a)%3D3a%5E%7B2%7D-2a%3B%20%5C%5C%0A%26%26(4)3a%5E%7B2%7D-(-3a)%3D3a%5E%7B2%7D%2B(%2B3a)%3D3a%5E%7B2%7D%2B3a%20.%0A%5Cend%7Beqnarray%7D$

例5.計(jì)算：

$%5Cscriptsize%5Cbegin%7Baligned%7D%26(1)%5Cquad3a%5E2-5a%2B(-7a%5E2)%3B%5C%5C%26(2)%5Cquad(%2Ba%5E2b)%2B(-ab%5E2)-(-2a%5E2b)%3B%5C%5C%26(3)%5Cquad%5Cfrac12x%5E3y%5E3%2B%5Cfrac13x%5E3y%5E2-%5Cleft(-%5Cfrac13x%5E3y%5E3%5Cright)%2B%5Cleft(-%5Cfrac12x%5E3y%5E2%5Cright)%3B%5C%5C%26(4)%5Cquad(%2B5a)%2B(-3b)%2B(%2B0.3c)%2B(-3a)%2B(%2B3b)%2B0.7c.%5Cend%7Baligned%7D$

【解】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26(1)3a%5E%7B2%7D-5a%2B(-7a%5E%7B2%7D)%3D3a%5E%7B2%7D-5a-7a%5E%7B2%7D%3D-4a%5E%7B2%7D-5a%3B%20%5C%5C%0A%26%26(2)(%2Ba%5E%7B2%7Db)%2B(-ab%5E%7B2%7D)-(-2a%5E%7B2%7Db)%20%5C%5C%0A%26%26%5Cquad%3D%2Ba%5E%7B2%7Db-ab%5E%7B2%7D%2B2a%5E%7B2%7Db-3a%5E%7B2%7Db-ab%5E%7B2%7D%3B%20%5C%5C%0A%26%26(3)%5Cfrac12x%5E3y%5E3%2B%5Cfrac13x%5E3y%5E3-%5Cleft(-%5Cfrac13x%5E3y%5E3%5Cright)%2B%5Cleft(-%5Cfrac12x%5E3y%5E2%5Cright)%20%5C%5C%0A%26%26%5Cquad%3D%5Cfrac%7B1%7D%7B2%7Dx%5E%7B3%7Dy%5E%7B3%7D%2B%5Cfrac%7B1%7D%7B3%7Dx%5E%7B3%7Dy%5E%7B2%7D%2B%5Cfrac%7B1%7D%7B3%7Dx%5E%7B2%7Dy%5E%7B3%7D-%5Cfrac%7B1%7D%7B2%7Dx%5E%7B3%7Dy%5E%7B3%7D%20%5C%5C%0A%26%26%5Cquad%3D%5Cfrac56x%5E%7B2%7Dy%5E%7B3%7D-%5Cfrac16x%5E%7B3%7Dy%5E%7B2%7D%3B%5C%5C%0A%26%26(4)(%2B5a)%2B(-3b)%2B(%2B0.3c)%2B(-3a)%2B(%2B3b)%2B0.7c%5C%5C%26%26%5Cquad%3D5a-3b%2B0.3c-3a%2B3b%2B0.7c%3D2a%2Be.%0A%5Cend%7Beqnarray%7D$

習(xí)題3-4(2)

1、計(jì)算：

$%5Cscriptsize%5Cbegin%7Baligned%7D(1)%26(-5a)-(-7a)%3B%26(2)%26(%2B3a)-(%2B8a)%3B%5C%5C(3)%26(%2B5ab)-(-6ab)%3B%26(4)%26(-3a%5E3)-(-3a%5E3)%3B%5C%5C(5)%26(-%5Cfrac%7B1%7D%7B2%7Da%5E2)-(-%5Cfrac%7B1%7D%7B3%7Da%5E2)%3B%26(6)%26a%5E2b%5E3c-2a%5E2b%5E3c.%5Cend%7Baligned%7D$

2、做下列減法：

$%5Cscriptsize%5Cbegin%7Barray%7D%7Blll%7D(1)%26(%2B5ab)-(-6ac)%3B%26(2)(-5a)-(%2B7a%5E2)%3B%5C%5C(3)%26(-4ab%5E2)-(%2B4a%5E2b)%3B%26(4)(-9x%5E2)-(%2B9y%5E2)%3B%5C%5C(5)%26(%2B3a%5E2b%5E3)-(%2B3a%5E3b%5E2)%3B%26(6)3a%5E2b%5E2c-(-3ab%5E2c%5E2).%5Cend%7Barray%7D$

3、計(jì)算：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26(1)%203a%2B(%2B5a)-(-3a)%3B%20%20%5C%5C%0A%26%26(2)5a%5E2-(%2B6a%5E2)%2B(-3a%5E2)%3B%5C%5C%0A%26%26(3)3a%5E%7B2%7Db%2B2a%5E%7B2%7Db-(%2B6a%5E%7B2%7Db)%3B%20%20%5C%5C%0A%26%26(4)(-3a%5E%7B2%7D)-(%2B3a%5E%7B2%7D)-(-6a%5E%7B2%7D)%20%20%5C%5C%0A%26%26(5)(-5a%5E%7B3%7D)%2B(-3a%5E%7B2%7D)-(-3a)%3B%20%20%5C%5C%0A%26%26(6)3ab-(-5ab)%2B(-7ac).%0A%5Cend%7Beqnarray%7D$

4、計(jì)算：

$%5Cscriptsize%5Cbegin%7Baligned%7D%26(1)3a-(%2B5a)-(-7a)%3B%5C%5C%0A%26(2)(-5a)-(-4a)%2B(%2B7a)%3B%5C%5C%26(3)(%2B3a%5E2)%2B(-5a%5E2)-(-7a%5E2)%3B%5C%5C%26(4)%5Cfrac%7B1%7D%7B2%7Da%5E2b%5E3-%5Cleft(-%5Cfrac%7B1%7D%7B3%7Da%5E2b%5E3%5Cright)-%5Cleft(-%5Cfrac%7B1%7D%7B4%7Da%5E2b%5E3%5Cright).%5Cend%7Baligned%7D$

5、計(jì)算：

$%5Cscriptsize%5Cbegin%7Bgathered%7D%0A(1)(-8x%5E%7B2%7Dy)%2B(%2B10x%5E%7B2%7Dy)-(-3xy%5E%7B2%7D)%2B(-5xy%5E%7B2%7D)%3B%20%5C%5C%0A(2)(-7y%5E%7B2%7D)%2B(-4y)-(-y%5E%7B2%7D)-(%2B5y)%2B(-8y%5E%7B2%7D).%20%0A%5Cend%7Bgathered%7D$

【答案】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A3%E3%80%81%26%26(1)11a%2C%5Cquad(2)-4a%5E2%2C%5Cquad(3)-a%5E2b%2C%5Cquad(4)0%2C%5C%5C%26%26(5)-5a%5E3-3a%5E2%2B3a%2C%5Cquad(6)8ab-7ac%3B%5C%5C%0A4%E3%80%81%26%26(1)5a%2C%5Cquad(2)6a%2C%5Cquad(3)5a%5E2%2C%5Cquad(4)%5Cfrac%7B1.3%7D%7B1.2%7Da%5E2b%5E3%3B%5C%5C%0A5%E3%80%81%26%26(1)2x%5E2y-2xy%5E2%2C%5Cquad(2)-14y%5E2-9y.%0A%5Cend%7Beqnarray%7D$

3、多項(xiàng)式的加法和減法

【05】根據(jù)加法結(jié)合律，我們知道：a＋(b＋c＋d)＝a＋b＋c＋d? 。根據(jù)減法的運(yùn)算性質(zhì)，我們還知道：a－(b＋c＋d)＝a－b－c－d? 。

【06】所以做多項(xiàng)式的加法和減法，可以應(yīng)用下面的多項(xiàng)式加減法法則：

????????(ⅰ)加上一個(gè)多項(xiàng)式，可以依次加上這個(gè)多項(xiàng)式的各項(xiàng)。

????????(ⅱ)減去一個(gè)多項(xiàng)式，可以改變減式各項(xiàng)的符號(hào)，把它們依次加在被減式上。

例6.做下面的加法：

$%5Cscriptsize%5Cbegin%7Baligned%7D%26(1)%5Cquad(3a%5E3%2B2a%5E2%2B5a-7)%2B(-2a%5E3%2B3a%5E2-5a%2B4)%3B%5C%5C%26(2)%5Cquad(3a%2B2b-3c)%2B(5a-3b%2B2c).%5Cend%7Baligned%7D$

【解】

$%5Cscriptsize%5Cbegin%7Baligned%7D%0A%26(1)%20(3a%5E3%2B2a%5E2%2B5a-7)%2B(-2a%5E3%2B3a%5E2-5a%2B4)%20%20%5C%5C%0A%26%3D3a%5E%7B3%7D%2B2a%5E%7B2%7D%2B5a-7-2a%5E%7B3%7D%2B3a%5E%7B2%7D-5a%2B4%20%5C%5C%0A%26%3D3a%5E3-2a%5E3%2B2a%5E2%2B3a%5E3%2B5a-5a-7%2B4%20%5C%5C%0A%26%3Da%5E3%2B5a%5E2-3%3B%20%5C%5C%0A%26(2)(3a%2B2b-3c)%2B(5a-3b%2B2c)%20%26%20%5Ctext%7B.%7D%20%20%5C%5C%0A%26%3D3a%2B2b-3c%2B5a-3b%2B2c%20%5C%5C%0A%26%3D3a%2B5a%2B2b-3b-3c%2B2c%3D8a-b-c.%0A%5Cend%7Baligned%7D$

例7.計(jì)算：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26(1)%20(3a%5E%7B2%7D-5a)-(5a%5E%7B2%7D-7a)%3B%20%20%5C%5C%0A%26%26(2)%20(-3a%2B5b)-(-5a%2B7b)%3B%20%20%5C%5C%0A%26%26(3)(3a%2B2b-3c)-(5a-2b%2B3c)%3B%20%20%5C%5C%0A%26%26(4)3-(3a%5E%7B3%7D-5a-7)%3B%20%20%5C%5C%0A%26%26(5)%20(a%5E3-3a%5E2b%2B3ab%5E2-b%5E3)-(a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3)%3B%20%5C%5C%0A%26%26(6)%20(x%5E%7B3%7D-3x%5E%7B2%7Dy%2B3xy%5E%7B2%7D)-(x%5E%7B3%7D-3x%5E%7B2%7Dy-3xy%5E%7B2%7D-y%5E%7B3%7D).%20%0A%5Cend%7Beqnarray%7D$

【解】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A(1)%26%26(3a%5E2-5a)-(5a%5E3-7a)%5C%5C%0A%26%26%3D3a%5E2-5a-5a%5E2%2B7a%5C%5C%26%26%3D-2a%5E2%2B2a%3B%5C%5C%0A(2)%26%26(-3a%2B5b)-(-5a%2B7b)%5C%5C%26%26%20%3D-3a%2B5b%2B5a-7b%20%20%5C%5C%0A%26%26%3D2a-2b%3B%20%5C%5C%0A(3)%26%26(3a%2B2b-3c)-(5a-2b%2B3c)%20%5C%5C%0A%26%26%3D3a%3D2h-3c-5a%2B2h-3a%20%5C%5C%0A%26%26%3D-2a%2B4b-6c%3B%20%5C%5C%0A(4)%26%263-(3a%5E2-5a-7)%5C%5C%26%26%3D3-3a%5E2%2B5a%2B7%20%5C%5C%0A%26%26%3D3a%5E2%2B5a%2B10%3B%20%5C%5C%0A(5)%26%26(a%5E3-3a%5E2b%2B3ab%5E2-b%5E3)-(a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3)%20%5C%5C%0A%26%26%3Da%5E3-3a%5E2b%2B3ab%5E2-b%5E3-a%5E3-3a%5E2b-3ab%5E2-b%5E3%20%5C%5C%0A%26%26%3D-6a%5E%7B2%7Db-2b%5E%7B3%7D%3B%20%5C%5C%0A(6)%26%26(x%5E3-3x%5E2y%2B3xy%5E2)-(x%5E3-3x%5E2y-3xy%5E2-y%5E3)%20%5C%5C%0A%26%26%3Dx%5E%7B3%7D-3x%5E%7B2%7Dy%2B2xy%5E%7B2%7D-x%5E%7B3%7D%2B3x%5E%7B2%7Dy%2B3xy%5E%7B2%7D%2By%5E%7B3%7D%20%5C%5C%0A%26%26%3D6xy%5E%7B2%7D%2By%5E%7B3%7D.%0A%5Cend%7Beqnarray%7D$

例8.計(jì)算：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26(1)(3a%2B5b)%2B(5a-4b)-(2a-3b)%3B%5C%5C%0A%26%26(2)(-a%5E3%2B3a%5E2-7a%2B5)%2B(5a%5E2-6a)-(a%5E2-4a%2B7)%3B%5C%5C%0A%26%26(3)%5Cleft(%5Cfrac13a%5E3-2a%5E2-%5Cfrac12a-6%5Cright)-%5Cleft(%5Cfrac13a%5E3-5%5Cright)-%5Cleft(%5Cfrac12a%5E3-4a-7%5Cright)%3B%5C%5C%0A%26%26(4)(0.3x%5E3-x%5E3y%2Bxy%5E2-y%5E2)-(-0.5x%5E3-x%5E2y%2B0.3xy%5E2)%2B(1.2x%5E3-1.2y%5E3).%0A%5Cend%7Beqnarray%7D$

【解】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A(1)%26%26(3a%2B5b)%2B(5a-4b)-(2a-3b)%20%5C%5C%0A%26%26%3D3a%2B5b%2B5a-4b-2a%2B3b-6a%2B4b%3B%20%5C%5C%0A(2)%26%26(-a%5E3%2B3a%5E2-7a%2B5)%2B(5a%5E2-6a)-(a%5E3-5)%20%5C%5C%0A%26%26%3D-a%5E%7B3%7D%2B3a%5E%7B2%7D-7a%2B5%2B5a%5E%7B2%7D-6a-a%5E%7B3%7D%2B4a-7%20%5C%5C%0A%26%26%3D-2a%5E%7B3%7D%2B8a%5E%7B2%7D-9a%2B2%3B%5C%5C%0A(3)%26%26%5Cleft(%5Cfrac13a%5E3-2a%5E3-%5Cfrac12a-6%5Cright)-%5Cleft(%5Cfrac13a%5E2-5%5Cright)%20-%5Cleft(%5Cfrac%7B1%7D%7B2%7Da%5E%7B3%7D-4a-7%5Cright)-%5Cleft(36-69%2B96%5Cright)%5Cquad(8)%20%5C%5C%0A%26%26%3D%5Cfrac13a%5E3-2a%5E3-%5Cfrac12a-6-%5Cfrac13a%5E3%2B5-%5Cfrac12a%5E3%2B4a%2B7%20%5C%5C%0A%26%26%3D-%5Cfrac16%5Cboldsymbol%7Ba%7D%5E%7B3%7D-%5Cfrac73a%5E%7B3%7D%2B%5Cfrac72a%2B6%3B%5C%5C%0A(4)%26%26(0.3x%5E3-x%5E2y%2Bxy%5E2-y%5E3)-(-0.5x%5E3-x%5E2y%2B0.3ay%5E2)%2B(1.2x%5E3-1.2y%5E3)%20%5C%5C%0A%26%26%3D0.3x%5E3-x%5E2y%2Bxy%5E3-y%5E3%2B0.5x%5E3%2Bx%5E2y%20-0.3xy%5E2%2B1.2x%5E3-1.2y%5E3%20%5C%5C%0A%26%26%3D2x%5E3%2B0.7xy%5E3-2.2y%5E3.%0A%5Cend%7Beqnarray%7D$

習(xí)題3-4(3)

1、計(jì)算：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26%5Ctext%7B(1)%7D%20(2x%5E%7B3%7D-3x%5E%7B2%7D%2B6x%2B5)%2B(x%5E%7B3%7D-6x%2B9)%3B%20%20%5C%5C%0A%26%26%5Ctext%7B(2)%7D%20(2a%5E%7B3%7D%2B5a%5E%7B2%7D%2B3a-1)%2B(3-8a%2B2a%5E%7B2%7D-6a%5E%7B3%7D)%3B%20%20%5C%5C%0A%26%26%5Ctext%7B(3)%7D%20(%2B3a%5E%7B2%7D%2Bb%5E%7B2%7D-5ab)%2B(4ab-b%5E%7B2%7D%2B7a%5E%7B2%7D)%3B%20%20%5C%5C%0A%26%26%5Ctext%7B(4%7D%20)%5Cleft(%5Cfrac%7B2%7D%7B3%7Dx%5E%7B2%7D-%5Cfrac%7B5%7D%7B6%7Dxy%2B%5Cfrac%7B3%7D%7B4%7Dy%5E%7B2%7D%5Cright)%2B%5Cleft(%5Cfrac%7B5%7D%7B12%7Dx%5E%7B2%7D-%5Cfrac%7B4%7D%7B3%7Dxy-%5Cfrac%7B7%7D%7B4%7Dy%5E%7B2%7D%5Cright)%20%2B%5Cleft(%5Cfrac%7B1%7D%7B2%7Dx%5E%7B2%7D-y%5E%7B2%7D%2B%5Cfrac%7B5%7D%7B4%7Dxy%5Cright).%0A%5Cend%7Beqnarray%7D$

2、做下列加法：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26(1)(3a%5E3-5a%5E2-a%2B4)%2B(-2a%5E4-5a%5E2%2Ba-3)%2B(-3a%5E3%2B5a-7)%3B%5C%5C%0A%26%26(2)(-3a%5E2-5b%5E2%2B3a%5E2)%2B%5Cleft(%5Cfrac%7B1%7D%7B2%7Da%5E2-%5Cfrac%7B1%7D%7B3%7Db%5E2-3c%5E2%5Cright)%2B%5Cleft(1%5Cfrac%7B1%7D%7B2%7Da%5E%7B2%7D%2B%5Cfrac%7B2%7D%7B3%7Db%5E%7B2%7D%2B%5Cfrac%7B1%7D%7B4%7Dc%5E%7B2%7D%5Cright)%3B%5C%5C%0A%26%26(3)(-0.3x%5E3y%2B0.5x%5E2y%5E2%2B3.1xy%5E3%2B0.4y%5E4)%2B(-1.2x%5E4-0.13x%5E3y%2B0.36xy%5E3%2B3y%5E4)%5C%5C%26%26%2B(3.2x%5E4-3.3x%5E3y%2B2.2x%5E2y%5E2-y%5E4)%3B%5C%5C%0A%26%26(4)(3a%5E2b-5ab%5E2%2B3b%5E3)%2B(a%5E3-3a%5E2b-5ab%5E2-2b%5E3)%2B(-a%5E3%2B10ab%5E2-b%5E3).%0A%5Cend%7Beqnarray%7D$

3、做下列減法：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%26(1)(6a%2B10b)-(2a%2B13b)%3B%5C%5C%0A%26%26(2)(2a-2b%2B4c)-(-2a-6b%2B4c)%3B%5C%5C%0A%26%26(3)(3a%5E2-5a%2B7)-(-3a%5E2-5a%2B7)%3B%5C%5C%0A%26%26(4)(3a%5E2-5ab%2B6b%5E2)-(3a%5E2%2B5ab-6b%5E2)%3B%5C%5C%0A%26%26(5)(ax%2Bbx%2Bay%2Bby)%3D(ax-bx-ay%2Bby)%3B%5C%5C%0A%26%26(6)(-3x%5E3-5x%5E2y%2B3xy%5E2-y%5E3)-(-2x%5E3%2B5x%5E2y-2y%5E5).%0A%5Cend%7Beqnarray%7D$

4、計(jì)算：

$%5Cscriptsize%5Cbegin%7Barray%7D%7Bll%7D(1)(3a%2B5b)%2B(5a-7b)-(2a-4b)%3B%5C%5C(2)(a%5E3-2a%5E2%2Ba-7)-(5a%5E2-7a%2B8)%2B(a%5E3-3a%5E2-5)%3B%5C%5C(3)(-x%5E3-3x%5E2%2B7x-8)-(3x%5E3-2x%5E3-5x%2B4)-(-x%5E3-2x%5E2%2B2)%3B%5C%5C(4)(x%5E3-3x%5E2y%2B3xy%5E2-y%5E3)-(x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3)-(6x%5E2y).%5Cend%7Barray%7D$

【答案】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A1%E3%80%81%26%26(1)3x%5E3-3x%5E2%2B14%2C%5Cquad(2)-4a%5E3%2B7a%5E2-5a%2B2%2C%20%5C%5C%0A%26%26(3)10a%5E2-ab%2C%5Cquad(4)%5Cfrac%7B19%7D%7B12%7Dx%5E2-%5Cfrac%7B11%7D%7B12%7Dxy-2y%5E2%3B%20%5C%5C%0A2%E3%80%81%26%26(1)%5Cquad-2a%5E4-10a%5E2%2B5a-6%5Ctext%7B%2C(2)%7D-a%5E2-4%5Cfrac23b%5E2%2B%5Cfrac14c%5E2%5Ctext%7B%2C%7D%20%5C%5C%0A%26%26(3)2x%5E4-3.73x%5E3y%2B2.7x%5E2y%5E2%2B3.46xy%5E3%2B2.4y%5E4%2C(4)0%3B%5C%5C%0A3%E3%80%81%26%26(1)4a-3b%2C%20%5Cquad(2)4a%2B4b%2C%5Cquad(3)6a%5E2%2C%5Cquad(4)-10ab%2B12b%5E2%2C%5C%5C%26%26(5)2bx%2B2ay%2C%20(6)-x%5E3-10x%5E2y%2B3xy%5E2%2By%5E3%3B%5C%5C%0A4%E3%80%81%26%26(1)6a%2B2b%2C%20(2)2a%5E3-10a%5E2%2B8a-20%2C%5C%5C%0A%26%26(3)-3x%5E3%2Bx%5E3%2B12x-14%5Cquad(4)-12x%5E2y-2y%5E3.%0A%0A%5Cend%7Beqnarray%7D$

4、多項(xiàng)式加減的直式運(yùn)算

【07】在做多項(xiàng)式的加減法時(shí)，為了便于合并同類項(xiàng)，我們也可以用直式來進(jìn)行演算。

例9.計(jì)算：(10x3－6x2＋5x－4)＋(9x3－2x2＋4x＋2)? 。

【解】用直式演算：

【注意】用直式迸行加法演算時(shí)，首先要把第一個(gè)加式按照某一字母的降冪（或升冪）整理排列，其他的加式排在下面，要注意對(duì)齊同類項(xiàng)，這樣，合并同類項(xiàng)時(shí)只要注意進(jìn)行直行的系數(shù)的加法，寫出對(duì)應(yīng)的同類項(xiàng)來就是了。

【注意】用直式進(jìn)行加法演算時(shí)，最后仍應(yīng)列出橫式來。

例10.計(jì)算：(8x3－6x2＋5x－12)＋(－4x2＋3x－8)＋(－5x3＋5x＋7)? 。

【解】用直式演算：

【注意】用直式進(jìn)行加法演算，如果有一些加式缺少某些冪的項(xiàng)時(shí)，可以空出相應(yīng)地位，務(wù)使同類項(xiàng)上下對(duì)齊，這樣才便于演算。

例11.計(jì)算：(3a2b－5a3＋b3)＋(6a3－7ab2－2b3)＋(3a3＋5a2b＋7ab2)? 。

【解】

例12.計(jì)算： $%5Cscriptsize%5Cbegin%7Baligned%7D%5Cleft(%5Cfrac12a%5E2%2B%5Cfrac13a-%5Cfrac14%5Cright)%2B%5Cleft(%5Cfrac13a%5E2-%5Cfrac14a%2B%5Cfrac15%5Cright)%2B%5Cleft(1%5Cfrac14a%5E2-0.3a%2B1%5Cright)%5Cend%7Baligned%7D$ ? 。

【解】

例13.計(jì)算：(3＋x2－4x)－(5x一8十3x2)? 。

【解】

【注意】同加法的直式寫法一樣，先要把被減式按照一個(gè)字母的降(或升)冪進(jìn)行排列，再將減式的各項(xiàng)寫在被減式的下面，使同類項(xiàng)互相對(duì)齊，然后在心中把減式各項(xiàng)的性質(zhì)符號(hào)換成相反符號(hào)后，按加法合并同類項(xiàng).最后還必須寫出一個(gè)橫式表示結(jié)果。

例14.計(jì)算：(3x?－2x2＋x－3)－(4x3－x2＋5)? 。

【解】

例15.計(jì)算：(5a?＋2a2b2＋ab3－3a3b)－(5a2b－2ab2＋3a2b2＋b?)? 。

【解】

習(xí)題3-4(4)

用直式進(jìn)行演算：

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%261%E3%80%81(2x%5E3-16%2Bx%5E4-2x)%2B(x%2B2)%2B(6x%5E2%2B8x%2B7x%5E4).%5C%5C%0A%26%262%E3%80%81(2x-14x%5E3-7x%5E2%2B5)%2B(5%2B9x%5E2-2x%5E3%2Bx)%2B(-4x%5E2-3%2B2x%5E3%2B5x).%5C%5C%0A%26%263%E3%80%81(2x%5E%7B3%7D-2x%5E%7B2%7D%2Bx%5E%7B4%7D)%2B(2x%5E%7B2%7D%2B3x%5E%7B4%7D-4)%2B(-3x%5E%7B3%7D-3x-5).%20%5C%5C%0A%26%264%E3%80%81(12ab-6a%5E2%2B10b%5E2)%2B(2a%5E2-3ab%2B2b%5E2)%2B(-8ab%2Ba%5E2-5b%5E2).%20%5C%5C%0A%26%265%E3%80%81(x%5E2-3xy-y%5E2)%2B(x%5E2%2B2xy%2By%5E2)%2B(-2x%5E2-xy)%20%20%5C%5C%0A%26%266%E3%80%81%5Cleft(%7B%5Cfrac%7B2%7D%7B3%7D%7Dx%5E%7B2%7D%2Bxy%2B%7B%5Cfrac%7B3%7D%7B2%7D%7Dy%5E%7B2%7D%5Cright)%2B%5Cleft(-%7B%5Cfrac%7B1%7D%7B3%7D%7Dx%5E%7B2%7D-%7B%5Cfrac%7B1%7D%7B2%7D%7Dxy-%7B%5Cfrac%7B1%7D%7B2%7D%7Dy%5E%7B2%7D%5Cright)%2B(x%5E%7B2%7D-y%5E%7B2%7D).%20%20%5C%5C%0A%26%267%E3%80%81%5Cleft(%5Cfrac%7B2%7D%7B3%7Dx%5E%7B3%7D-%5Cfrac%7B1%7D%7B4%7Dx%5E%7B2%7D%2B%5Cfrac%7B1%7D%7B3%7Dx-5%5Cright)%2B%5Cleft(-%5Cfrac%7B1%7D%7B3%7Dx%5E%7B3%7D-%5Cfrac%7B1%7D%7B2%7Dx%5E%7B2%7D%2B%5Cfrac%7B2%7D%7B3%7Dx-%5Cfrac%7B1%7D%7B3%7D%5Cright)%20%2B%5Cleft(x%5E3-%5Cfrac13%5Cright).%5C%5C%0A%26%268%E3%80%81(a%5E4%2B4a%5E2b%2B6a%5E2b%5E2%2B4ab%5E3%2Bb%5E4)%2B(a%5E4-4a%5E3b%2B6a%5E2b%5E2-4ab%5E2%2Bb%5E4).%5C%5C%0A%26%269%E3%80%81(-0.3a%5E9-0.2a%5E2-0.1a-0.5)%2B(-0.2a%5E3-0.3a%5E2%2B0.4a-0.5)%5C%5C%26%26%5Cquad%2B(-0.5a%5E9%2B0.5a%5E2-0.5a%2B1).%5C%5C%0A%26%2610%E3%80%81%5Cleft(-0.3a%5E%7B2%7D%2B%5Cfrac%7B1%7D%7B2%7Dab-0.4b%5E%7B2%7D%5Cright)%2B%5Cleft(%5Cfrac%7B1%7D%7B3%7Da%5E%7B2%7D-0.5ab%2B%5Cfrac%7B1%7D%7B3%7Db%5E%7B2%7D%5Cright).%20%20%5C%5C%0A%26%2611%E3%80%81%20(4x%2B2y-3z)-(4x-2y%2B3z)%20%20%5C%5C%0A%26%2612%E3%80%81%20(4x%5E3%2Bx%5E2-5x-12)-(-x%5E3%2Bx%5E2-4x%2B11).%20%20%5C%5C%0A%26%2613%E3%80%81%20(12x%5E7-8x%5E5%2B4x%5E4-12x%5E3)-(-3x%5E6%2B2x%5E4-x%5E3%2B3x%5E2)_*%20%20%5C%5C%0A%26%2614%E3%80%81(a%5E%7B2%7D-ab%2B2b%5E%7B2%7D)-(a%5E%7B2%7D%2Bab-2b%5E%7B2%7D).%20%20%5C%5C%0A%26%2615%20%E3%80%81(8-6x%2B4x%5E%7B3%7D%2B5x%5E%7B2%7D)-(3x%5E%7B3%7D-3-2x%5E%7B3%7D-7x).%5C%5C%0A%26%2616%E3%80%81(2a%5E3-6a%5E2b%2B6ab%5E2-2b%5E3)-(a%5E3-7a%5E2b-3b%5E3).%5C%5C%0A%26%2617%E3%80%81(a%5E3-b%5E3)-(a%5E3-3a%5E2b%2B3ab%5E2-b%5E3)_%5Cbullet%5C%5C%0A%26%2618%E3%80%81%5Cleft(%5Cfrac%7B3%7D%7B2%7Da%5E3-%5Cfrac%7B3%7D%7B4%7Da%2B%5Cfrac%7B5%7D%7B6%7D%5Cright)-%5Cleft(%5Cfrac%7B8%7D%7B15%7Da%5E3-%5Cfrac%7B1%7D%7B10%7Da%5E2-%5Cfrac%7B2%7D%7B9%7D%5Cright).%0A%5Cend%7Beqnarray%7D$

【答案】

$%5Cscriptsize%5Cbegin%7Beqnarray%7D%0A%26%261.%5Cquad8x%5E4%2B2x%5E3%2B6x%5E2%2B7x-14%3B%5Cquad2.%5Cquad-14x%5E3-2x%5E2%2B8x%2B7%3B%5C%5C%0A%26%263.%5Cquad4x%5E4-x%5E3-3x-9%3B%5Cquad4.%5Cquad-3a%5E2%2Bab%2B7b%5E2%3B%5Cquad5.%5Cquad-2xy%3B%5C%5C%0A%26%266.%5Cquad%5Cfrac%7B4%7D%7B3%7Dx%5E2%2B%5Cfrac%7B1%7D%7B2%7Dxy%3B%5Cquad7.%5Cquad%5Cfrac%7B4%7D%7B3%7Dx%5E3-%5Cfrac%7B3%7D%7B4%7Dx%5E2%2Bx-5%5Cfrac%7B2%7D%7B3%7D%3B%5Cquad8.%5Cquad2a%5E4%2B12a%5E2b%5E2%2B2b%5E4%3B%5C%5C%0A%26%269.%5Cquad-a%5E3-0.2a%3B%5Cquad10.%5Cquad%5Cfrac%7B1%7D%7B30%7Da%5E2-%5Cfrac%7B1%7D%7B15%7Db%5E2%3B%5Cquad11.%5Cquad4y-6z%3B%5Cquad12.5x%5E3-x-22%3B%5C%5C%26%2613.%5Cquad12x%5E7%2B3x%5E6-8x%5E5%2B2x%5E4-11x%5E3-3x%5E2%3B%5Cquad14.%5Cquad-2ab%2B4b%5E2%3B%5C%5C%26%2615.%5Cquad6x%5E3%2B2x%5E2%2Bi%2B11%3B%5Cquad16.%5Cquad%20a%5E3%2Ba%5E2b%2B6ab%5E2%2Bb%5E3%3B%5Cquad17.%5Cquad3a%5E2b-3ab%5E2%3B%5C%5C%26%2618.%5Cquad%5Cfrac%7B29%7D%7B30%7Da%5E3%2B%5Cfrac%7B1%7D%7B10%7Da%5E2-%5Cfrac%7B3%7D%7B4%7Da%2B%5Cfrac%7B19%7D%7B18%7D.%0A%0A%5Cend%7Beqnarray%7D$

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【種花家務(wù)·代數(shù)】1-3-04整式的加減法『數(shù)理化自學(xué)叢書6677版』

習(xí)題3-4(1)

習(xí)題3-4(2)

習(xí)題3-4(3)

習(xí)題3-4(4)