2021年七年级数学下册第一章知识点总结.pdf
七年级数学下册第一章知识点总结七年级数学下册第一章知识点总结第一章整式的乘除水塘中学李学英一、幂的运算性质 n m n+m 1、同底数幂相乘：底数不变，指数相加。a?a=a n m nm(a)=a 2、幂的乘方：底数不变，指数相乘。(ab)=a b 3、积的乘方：把积中的每一个因式各自乘方，再把所得的幂相乘。a 4、零指数幂：任何一个不等于0 的数的 0 次幂等于 1。=1（a 0）注意 00没有意义。5、负整数指数幂：a（p 正整数，a 0）n m n-m 6、同底数幂相除：底数不变，指数相减。a a=a注意：以上公式的正反两方面的应用。常见的错误：a 2?a 3=a 6，(a 2)3=a 5，(ab)3=ab 3，a 6a 2=a 3，a 2+a 2=2a 4 二、单项式乘以单项式：系数相乘，相同的字母相乘，只在一个因式中出现的字母则连同它的指数作为积的一个因式。三、单项式乘以多项式：运用乘法的分配率，把这个单项式乘以多项式的每一项。四、多项式乘以多项式：连同各项的符号把其中一个多项式的各项乘以另一个多项式的每一项。(a+b)(m+n)=am+an+bm+bn五、平方差公式两数的和乘以这两数的差，等于这两数的平方差。即：一项符号相同，另一项符号相反，等于符号相同的平方减去符号相反的 ()()a+b a-b=a-b 平方。精品w o r d 可编辑资料-第 1 页，共 4 页-六、完全平方公式两数的和（或差）的平方，等于这两数的平方和再加上（或减去）两数积的2 倍。(a+b)2=a 2+b 2+2ab(a-b)2=a 2+b 2-2ab常见错误：(a+b)2=a 2+b 2(a-b)2=a 2-b 2七、单项除以单项式：把单项式的系数相除，相同的字母相除，只在被除式中出现的字母则连同它的指数作为商的一个因式。八、多项式除以单项式：连同各项的符号，把多项式的各项都除以单项式。幂的乘方 1.-a?(-a)；(a)?a；(a)?3?；?y?a 2=a 14；2.若（a 3）n（a n）m（m，n 都是正整数），则m _ 12?3.计算?-x y?2?的结果正确的是（）B.1x y C.-1x 5y 3 D.-1x y 4.判断题：（对的打“”，错的打“”）5.若 m、n、p 是正整数，则(a m?a n)p 等于（）a 2+a 3=a 5()x 2?x 3=x 6()（x 2)3=x 5（）a 4?a 2=a 8（）mp+np m np nmp A a?a Ba Ca Da 6.计算题（1）-p?(-p)4（2）（a 2）3（3）（-a 2）3（4）(-6)（5）?2?3?3?精品w o r d 可编辑资料-第 2 页，共 4 页-文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7（6）（x 2）37；7.若 x?x=2，求 x、=16,则 x=_.积的乘方 1.(-310)-(2x 2y 4)3_；(-ax 2)2=(a 3)(_；(-1ab 2c)2=_；?-2x?a 2=a 14?2?3?(-3)200=；(3a )+(a 2)2?a 2n n 2.若 x=3,y=7，则(xy)=；(x 2y 3)n 3.4.计算（3a 2b 3）3，正确的结果是（）A 27a 6b 9 B 27a 8b 27 C 9a 6b 9 D 27a 5b 6 5.(-a)3?(a 2)?(-a)2的结果正确的是（）6.判断题：；(6xy)2=12x 2y 2（）;(-2b 2)2=-4b 4（）；a m?a 4=a 4m（）(ab 3)2=ab 6（）7计算题：（每题4 分，共 28 分）（1）x?x（2）x y 2332(x y)(xy)（5）（3）(-3pq)（4）-（xy 2z）4（6）(xy 3n)+(xy 6)8.已知 x n 5，y n 3，求（xy）2n 的值同底数幂的乘除法 1.下列运算结果正确的是()2x 3-x 2=x x 3(x5)2=x13(-x)6(-x)3=x3(0.1)-210-?1=10 A.B.C.D.2.（abc）5（abc）3=。x n+1x n-1(xn)2=.3.(m-n)2?(m-n)32(m-n)4=_.4如果 9m+3?27m+134m+7=81,那么 m=_.5.若 3m=5,3n=4,则 32m-n 等于()精品w o r d 可编辑资料-第 3 页，共 4 页-文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7 A.25 B.6 C.21 D.20 6.若 102y=25,则 10-y 等于()7.若 a=-0.32,b=-3-2,c=(-)-2,d=(-)0,则()C.-5625 (1)()0+(-1)3+()-3-3;(2)(-27)-15?(-9)20(-3)-7;(3)(x2y)6(x2y)3(4)(x+y)2n 4(-x-y)2n+1(n是正整数).9.若(3x+2y-10)0无意义,且 2x+y=5,求 x、y 的值.(6 分)整式的乘法及平方差公式与完全平方公式的运算 1.3x(x-2y);-4a(a-2b)-4x 2(1xy+2y)2 2(x2-2x+1)(-3x)(-x y+32xy)(2x+5)(x-3)=;(x-3y)(x-5y)=；（2x-3y)(3x-5y)=2.2x 2y(1 3xy+y)的计算结果是()2 A.2x 2y 46x 3y 2+x 2y B.x 2y+2x 2y 4 C.2x 2y 4+x 2y 6x 3y 2 D.6x 3y 2+2x 2y 4 3.计算(2x-1)(5x+2)的结果是()A.10 x 2-2 B.10 x2-5x-2 C.10 x2+4x-2 D.10 x2-x-2 4.计算(a-3)(a+3)2a(-2ab+ab 2);y 2(y-y 2);3x 2(y xy 2(-4xy)?(xy+3x 2y);(-xy)(x 2y-xy 2+y);1236(3x2y)(2x 3y);(3x2y)(3x+2y)(3x+2)(-x-2);(a+3)(a+3)精品w o r d 可编辑资料-第 4 页，共 4 页-文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 HC2A2M3X4M7 ZG9N6W10J5P7文档编码:CB9W5I1H7G4 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