湖南省新邵县酿溪中学七年级数学下册 提公因式法第2课时课件 新版湘教版1

1、提公因式法,2,1,多项式的第一项系数为负数时,先提,取,号，注意多项式的各项变号,复习,提公因式法,2,公因式的系数是多项式各项,_,3,字母取多项式各项中都含有,的,_,4,相同字母的指数取各项中最,小的一个,即,_,系数的最大公约数,相同的字母,最低次幂,想一想,提公因式法分解因式与单项式,乘多项式有什么关系,把下列各式分解因式,1,8m n + 2mn,2,a,b,5,ab + 9b,3,3,ma,6,ma,12,ma,2,2,2,3,2mn(4m+1,b(a,5a + 9,2,3ma(a,2a + 4,2,6m,3,n,2,4m,2,n,3,10m,2,n,2,解：原式,2mn,3m

2、,2,n,2mn,2,5mn,2m,2,n,2,3m,2n,5,6m,3,n,2,4m,2,n,3,10m,2,n,2,x,1,x,2,x,1,x,1,x,2,x,1,解：原式,x,2,x,1,x,1,x,1,x,2,x,1,2x,2x,x,2,x,1,在下列各式等号右边的括号前,填入,或“”号，使等式成立,1,a-b) =_(b-a); (2) (a-b,2,_(b-a,2,3) (a-b,3,_(b-a,3,4) (a-b,4,_(b-a,4,5) (a+b,5,_(b+a,5,6) (a+b,6,_(b+a,6,7) (a+b) =_(-b-a,8) (a+b,2,_(-a,b,2,由此

3、可知规律,1)a-b,与,a+b,互为相反数,a-b,n,(b-a,n,n,是偶数,a-b,n,-(b-a,n,n,是,奇数,2) a+b,与,b+a,互为相同数,a+b,n,(b+a,n,n,是整数,a+b,与,a-b,互,为相反数,a-b,n,(a+b,n,n,是偶数,a-b,n,-(a+b,n,n,是奇数,练习一,1,在下列各式右边括号前添上适当的符号,使左边与右边相等,1) a+2 = _(2+a,2) -x+2y = _(2y-x,3) (m-a,2,_(a-m,2,4) (a-b,3,_(-a+b,3,5) (x+y)(x-2y)= _(y+x)(2y-x,2,判断下列各式是否正确

4、,1) (y-x,2,-(x-y,2,2) (3+2x,3,-(2x+3,3,3) a-2b = -(-2b+a,4) -a+b = -(a+b,5) (a-b)(x-2y) = (b-a)(2y-x,例,1,把,a(x-3)+2b(x-3,分解因式,解,a(x-3)+2b(x-3,（,分析,多项式可看成,a(x-3,与,2b(x-3,两项,公因式为,x-3,经典例题,例,2,把,a(x-y)+b(y-x,分解因式,解,a(x-y)+b(y-x,a(x-y)-b(x-y,y,分析：多项式可看成,a(x-y,与,b(y-x,两项。其中,X,y,与,y-x,互为相反数,可,将,b(y-x,变为,b

5、(x-y,则,a(x-y,与,b(x-y,公因式为,x-y,例,3,把,6(m-n,3,12(n-m,2,分解因式,解,6(m-n,3,12(n-m,2,6(m-n,3,12(m-n,2,6(m-n,2,m-n-2,分析：其中,m-n,与,n-m,互为相反数,可将,12,n-m,2,变为,12(m-n,2,则,6(m-n,3,与,12(m-n,2,公因式为,6(m-n,2,例,4,把,6,x,y,y,x,2,9,x,y,3,分解因式,解,6,x,y,(y,x,2,9,x,y,3,6,x,y,(x,y,2,9,x,y,3,3(x-y,2,2(x+y)-3(x-y,3(x-y,2,2x+2y-3x

6、+3y,3(x-y,2,x+5y,3(x-y,2,5y-x,例,4,把,12AB,2,B+C)-18A,2,B(B+C,分解因式,试一试,1) 2a(y-z)-3b(z-y,2) p(a,2,b,2,q(a,2,b,2,2) 5,x,a,b,2,10,y,b,a,2,3,2,3,12,6,m,n,n,m,1,x,y,b,y,x,a,4,a,a,b,a,b,a,a,b,2,5,mn,m,n,m,n,m,2,6) 2,a,3,2,a,3,7,a,x,a,b,a,x,c,x,a,练习二分解因式,小结,两个,只有符号不同,的多项式是否有关系,有如下判断方法,1,当,相同字母前的符号相同,时,则两个多项式相等,如,a-b,和,b+a,即,a-b = -b+a,2,当,相同字母前的符号均相反,时,则两个多项式互为相反数,如,a-b,和,b-a,即,a-b =,b-a,例,7,利用因式分解计算,14,99,19,99,19,13,99,19,72,99,19,29,1,81,13,37,39,2,思维拓展训练,的值,求,已知,x,x,x,x,14,8,3,1,7,4,1,2,2,的值,求,已知,0,2,2,a,c,b,c,b,a,c,b,c,b,a,a,c,b,a,试一试,