十字相乘法-课件（ppt·精·选）.ppt

知识回顾????提公因式法: ma+mb+mc=m(a+b+c)?运用公式法: a2-b2=(a+b)(a-b)a2±2ab+b2=(a ±b)2(5) 3ax2+6ax+3a(4) x5 - x3(1) x4 - y4(2)(y2 + x2 )2 - 4x2y2(6) 2ax2+6ax+4a(3) x4-8x2+:解:(1) x4 - y4=(x2+y2)(x2-y2) = (x2+y2)(x+y)(x-y)(2) (y2 + x2 )2 - 4x2y2 =(y2 + x2 +2xy) (y2 + x2 -2xy) =(x+y)2(x-y)2(3) x4-8x2+16=(x2-4)2 =(x+2)2(x-2)2(4) x5 - x3=x3(x2-1)=x3(x+1)(x-1)(5) 3ax2+6ax+3a=3a(x2+2x+1) =3a(x+1)2(6) 2ax2+6ax+4a=2a(x2+3x+2)=2a(x+1)(x+2)1.(x+2)(x+1)=xx22+3x+2+3x+233.(x-2)(x+1)=.(x-2)(x+1)=xx22-x-2-x-244.(x-2)(x-1)=.(x-2)(x-1)=xx22-3x+2-3x+222.(x+2)(x-1)=.(x+2)(x-1)=xx22+x-2+x-255.(x+2)(x+3)=.(x+2)(x+3)=xx22+5x+6+5x+666.(x+2)(x-3)=.(x+2)(x-3)=xx22-x-6-x-677.(x-2)(x+3)=.(x-2)(x+3)=xx22+x-6+x-688.(x-2)(x-3)=.(x-2)(x-3)=xx22-5x+6-5x+6(x+(x+aa)(x+)(x+bb))=x=x22+(+(a+ba+b)x+)x+abab请直接口答计算结果:(x+2)(x+1)xx22+3x+2+3x+2(x-2)(x+1)(x-2)(x+1)xx22-x-2-x-2(x-2)(x-1)(x-2)(x-1)xx22-3x+2-3x+2(x+2)(x-1)(x+2)(x-1)xx22+x-2+x-2(x+2)(x+3)(x+2)(x+3)xx22+5x+6+5x+6(x+2)(x-3)(x+2)(x-3)xx22-x-6-x-6(x-2)(x+3)(x-2)(x+3)xx22+x-6+x-6(x-2)(x-3)(x-2)(x-3)xx22-5x+6-5x+6(x+a)(x+b)(x+a)(x+b)==xx22+(a+b)x+ab+(a+b)x+ab================.(x+a)(x+b)=x2+(a+b)x+ab两个一次二项式相乘的积一个二次三项式整式的乘法反过来,得x2+(a+b)x+ab=(x+a)(x+b)一个二次三项式两个一次二项式相乘的积因式分解如果二次三项式x2+px+q中的常数项系数q能分解成两个因数a、b的积,而且一次项系数p又恰好是a+b,那么x2+px+q就可以进行如上的因式分解。)2)(1(???xx解:原式分析∵(+1) ×(+2)=+2 (+1)+(+2)=+3xx1?2?∴试一试:把x2+3x+2分解因式常数项一次项系数十字交叉线利用十字交叉线来分解系数,把二次三项式分解因式的方法叫做十字相乘法。