提出公因式与分组分解

提出公因式與分組分解

麗山國中王綉瑗製分配律甲×丙＋乙×丙＝(甲＋乙)×丙丙×甲＋丙×乙＝丙×(甲＋乙)

=提出公因式1因式分解下列各式：ax+bx=x(a+b)2x+bx=x(2+b)ax-3x=x(a-3)2x2-6x+4ax=2x(x-3+2a)學生演練1因式分解下列各式：x2+3x3y2+y3x2-9ax+15x學生演練1因式分解下列各式：x2+3x=x(x+3)3y2+y=y(3y+1)3x2-9ax+15x

=3x(x-3a+5)因式分解下列各式2：(x+7)x-5x=x(x+7-5)=x(x+2)(x-5)(x+5)-(x-5)=(x-5)(x+5-1)=(x-5)(x+4) 學生演練2因式分解下列各式：x(x-1)-xx(3x+6)-3x3(x+2)(x-4)-(x+2)(x+1)學生演練2因式分解下列各式：x(x-1)-x=x(x-1-1)=x(x-2)x(3x+6)-3x=x(3x+6-3)=x(3x+3)=3x(x+1)

3(x+2)(x-4)-(x+2)(x+1)=(x+2)[3(x-4)-(x+1)]=(x+2)(3x-12-x-1)=(x+2)(2x-13)分組提公因式3因式分解下列各式：ax2+bx-2ax-2b=(ax2+bx)-(2ax+2b)=x(ax+b)-2(ax+b)=(ax+b)(x-2)2.x2-3x-x+3=(x2-3x)-(x-3)=x(x-3)-(x-3)=(x-3)(x-1)3.x2-(a-b)x-ab=x2-ax+bx-ab=(x2-ax)+(bx-ab)=x(x-a)+b(x-a)=(x-a)(x+b)學生演練3因式分解下列各式：(x2-3x)+(x-3)22ax2-3x+2ax-32x2-3x+2x-32(ab-2)-(8a-b)學生演練3因式分解下列各式：(x2-3x)+(x-3)2=x(x-3)+(x-3)2=(x-3)(x+x-3)=(x-3)(2x-3)2ax2-3x+2ax-3=(2ax2-3x)+(2ax-3)=x(2ax-3)+(2ax-3)=(2ax-3)(x+1)2x2-3x+2x-3=(2x2-3x)+(2x-3)=x(2x-3)+(2x-3)=(2x-3)(x+1)2(ab-2)-(8a-b)=2ab-4-8a+b=2ab-8a-4+b=2a(b-4)+(b-4)=(b-4)(2a+1)因式分解下列各式4：x(x-1)-(1-x)=x(x-1)+(x-1)=(x-1)(x+1)(a-2b)-(a-2b)2=(a-2b)(1-a+2b)3.(2x+1)(x-1)-5(2x+1)=(2x+1)(x-1-5)=(2x+1)(x-6)4.(a+b)(a-3b)-(a+b)2=(a+b)(a-3b-a-b)=-4b(a+b)學生演練4因式分解下列各式：(x-y)-(y-x)2(2a+3b)2-3(2a+3b)(y-2)(y+2)+(2-y)(y+3)3(a-3)-(a2-3a)學生演練4因式分解下列各式：(x-y)-(y-x)2=(x-y)-(x-y)2

=(x-y)[1-(x-y)]=(x-y)(1-x+y)(2a+3b)2-3(2a+3b)=(2a+3b)(2a+3b-3)(y-2)(y+2)+(2-y)(y+3)=(y-2)(y+2)-(y-2)(y+3)=(y-2)[(y+2)-(y+3)]=-(y-2)3(a-3)-(a2-3a)=3(a-3)-a(a-3)=(a-3)(3-a)=-(a-3)2因式分解下列各式5：(a-2)x-(x2-2a)=ax-2x-x2+2a=(ax-x2)+(2a-2x)=x(a-x)+2(a-x)=(a-x)(x+2)2.x2-4(a+x)+ax=x2-4a-4x+ax=(x2-4x)+(ax-4a)=x(x-4)+a(x-4)=(x-4)(x+a)學生演練5因式分解下列各式：2a+(a2-4)x-2ax2a(ax-x2+1)-x(5a-2)2-(5a-2)(5a+2)(x+1)(x-2)+a(x+1)22xy+6x-3y-9a2+6xy+2ax-6x2-3ax-2ay學生演練52a+(a2-4)x-2ax2=2a+a2x-4x-2ax2=(2a+a2x)-(4x+2ax2)=a(2+ax)-2x(2+ax)=(2+ax)(a-2x)a(ax-x2+1)-x=a2x-ax2+a-x=(a2x-ax2)+(a-x)=ax(a-x)+(a-x)=(a-x)(ax+1)(5a-2)2-(5a-2)(5a+2)=(5a-2)[(5a-2)-(5a+2)]=(5a-2)(5a-2-5a-2)

=-4(5a-2)(x+1)(x-2)+a(x+1)2=(x+1)[(x-2)+a(x+1)]=(x+1)(x-2+ax+a)學生演練52xy+6x-3y-9=(2xy+6x)-(3y+9)