2019七年级整式奥数题经典题型汇总

..七年级整式奥数题经典题型汇编例1．求[x3-(x-1)2](x-1)展开后，x2项的系数．例3．化简(1+x)[1-x+x2-x3+…+(-x)n-1]，其中n为大于1的整数．例4．计算(1)(a-b+c-d)(c-a-d-b)；(2)(x+2y)(x-2y)(x4-8x2y2+16y4)．例5．设x，y，z为实数，且(y-z)2+(x-y)2+(z-x)2=(y+z-2x)2+(x+z-2y)2+(x+y-2z)2，例6．设g(x)=3x2-2x+1，f(x)=x3-3x2-x-1，求用g(x)去除f(x)所得的商q(x)及余式r(x)．例7．试确定a和b，使x4+ax2-bx+2能被x2+3x+2整除．例8．计算：(1)(a-2b+c)(a+2b-c)-(a+2b+c)2；(2)(x+y)4(x-y)4；(3)(a+b+c)(a2+b2+c2-ab-ac-bc)．例9．化简：(1)(2x-y+z-2c+m)(m+y-2x-2c-z)；(2)(a+3b)(a2-3ab+9b2)-(a-3b)(a2+3ab+9b2)；(3)(x+y)2(y+z-x)(z+x-y)+(x-y)2(x+y+z)×(x+y-z)．3．已知z2=x2+y2，化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z)．4．设f(x)=2x3+3x2-x+2，求f(x)除以x2-2x+3所得的商式和余式．例10.当,ab为何值时，多项式224618abab有最小值？并求出这个最小值。例11.若3(1)(2)(3)(1)(2)(1)xaxxxbxxcxd，求,,,abcd。例12.若2310aa，求1aa的值（提示：注意0a）；例13.已知xyza，xyyzzxb，求222xyz的值。例14.△ABC三边,,abc满足222abcabbcca，试判定△ABC的形状。