平方差公式和完全平方公式(讲义)课前预习1.(1)对于多项式(4)x和多项式(4)x,完全相同的项是________,只有符号不同的项是________;(2)对于多项式(4)x和多项式(4)x,完全相同的项是________,只有符号不同的项是________;(3)对于多项式()abc和多项式()abc,完全相同的项是_________,只有符号不同的项是__________.2.利用幂的运算法则证明22()()abab.证明过程如下:2222()()(___)(____)__________abab即22()()abab请你参照上面的方法证明22()()abab.3.计算:①()()abab;②2()ab;③2()ab.知识点睛1.平方差公式:___________________________.2.完全平方公式:_________________________;_________________________.口诀:首平方、尾平方,二倍乘积放中央.精讲精练1.填空:①22(4)(4)()()xx_________;②22(32)(32)()()abab__________;③22()()()()mnmn_____________;④112244xyxy=_______-_______=___________;⑤()()nnabab_______-_______=__________;⑥22(33)(33)()()abab;⑦22(33)(33)()()abab;⑧(m+n)(m-n)(m2+n2)=()(m2+n2)=()2-()2=_______;⑨22(23)()49xyxy;⑩22(3)()9xyyx.2.计算:①(8)(8)abab;②112233abba;③22(2)(2)(4)ababab;④10397;⑤2201520142016.3.①222(25)()2()()()xy_______________;②22211()2()()()32m___________;③212mnn_____________________=______________;④22()()xy________________;⑤22()()mn________________;⑥2(34)xy=2()______________________;⑦2142xy=2()______________________;⑧224xy_________2(2)xy.4.下列各式一定成立的是()A.222(2)42abaabbB.222()xyxyC.2221124abaabbD.22()()xyxyxy5.计算:①2(21)t;②22(2)4mnn;③2()abc;④2102.6.运用乘法公式计算:①2(2)4()()xyxyxy;②()()()()abababab;③(23)(23)xyxy;④()()abcabc;⑤3()ab;⑥()()abcabc;⑦2210298;⑧2222(1)(1)nn.7.若222(3)xyaxbxyy,则a=______,b=_________.8.若2222(2)4xyaxxyy,则a=______.9.若222()96axyxxyy,则a=______.10.若222()816xkyxxyy,则k=______.11.若229xaxyy是完全平方式,则a=______.12.若2244xxymy是完全平方式,则m=______.【参考答案】课前预习1.(1)x;4,-4;(2)-4;x,x;(3)b-c;a,-a2.略3.①22ab②222aabb③222aabb知识点睛1.22()()ababab2.222()2abaabb,222()2abaabb精讲精练1.①x,4,216x②3a,2b,2294ab③n,m,22nm④2(2)y,214x,221416yx⑤2()na,2b,22nab⑥3ab,3⑦3a,3b⑧22mn,2m,2n,44mn⑨23xy⑩3yx2.①2264ab②22149ba③4416ab④9991⑤13.①2x,2x,5y,5y,2242025xxyy②13m,13m,12,12,2111934mm③2211()2()22mnmnnn;222214mnmnn④xy,222xxyy⑤mn,222mmnn⑥3x-4y,2292416xxyy⑦142xy;2211644xxyy⑧(4)xy4.C5.①2441tt②24mmn③222222abcabacbc④104046.①245xyy②222abb③224129xyy④2222caabb⑤332233ababab⑥222222aabbacbcc⑦800⑧24n7.9;-68.±29.-310.-411.612.1