因式分解復(fù)習(xí)課

因式分解復(fù)習(xí)課知識(shí)要點(diǎn)：多項(xiàng)式-6x2+6xy+3x=-3x(2x-2y-1)二項(xiàng)式a2-b2=(a+b)(a-b)立方和差:a3±b3=(a±b)(a2+ab+b2)添項(xiàng):x4+4=x4+4x2+4-4x2=(x2+2+2x)(x2+2-2x)三項(xiàng)式完全平方式:a2±2ab+b2=(a±b)2十字相乘法:a2-29a+100=(a-25)(a-4)拆項(xiàng)法:x3-3x+2=x3-x-2x+2=(x-1)2(x+2)多于三項(xiàng)的多項(xiàng)式分組分解分組后提公因式:ma-mb+na-nb=(a-b)(m+n)分組后運(yùn)用公式:x2-y2-1+2y=(x+y-1)(x-y+1)分組后十字相乘:x2+2xy+y2+2x+2y-3=(x+y+3)(x+y-1)提取公因式:平方差：一、分解因式a(a+b)(a-b)2、(a-b)(x-y)-(b-a)(x+y)=2x(a-b)3、(a+b)2+2(a+b)-15=(a+b+5)(a+b-3)4、-1-2a-a2=-(a+1)25、x2-6x+9-y2=(x-3+y)(x-3-y)6、x2-4y2+x+2y=(x+2y)(x-2y+1)7、9x2+6xy+y2+3x+y=(3x+y)(3x+y+1)8、9x2+6xy+y2+3x+y-2=(3x+y+2)(3x+y-1)a(a2-b2)=1、a3-ab2=二、分解因式:1、72-2(13x-7)22、8a2b2-2a4b-8b3解:72-2(13x-1)2解:8a2b2-2a4b-8b3=2[62-(13x-7)2]=2(6+13x-7)(6-13x+7)=2(13x-1)(-13x+13)=-26(13x-1)(x-1)=2b(4a2b-a4-4b2)=-2b(a4-4a2b+4b2)=-2b(a2-2b)23、9a4-4a2+4a-1解:9a4-4a2+4a-1=9a4-(4a2-4a+1)=9a4-(2a-1)2=(3a2+2a-1)(3a2-2a+1)=(a+1)(3a-1)(3a2-2a+1)4、(x-1)(x+2)(x-3)(x+4)+24解:(x-1)(x+2)(x-3)(x+4)+24=(x2+x-2)(x2+x-12)+24=(x2+x)2-14(x2+x)+48=(x2+x-6)(x2+x-8)=(x+3)(x-2)(x2+x-8)4、a2+b2-c2-4d2-2ab+4cd三、練習(xí)：1、x6-y63、5(x2-2x)2-14(x2-2x)-32、x3+12x-6x2-85、2x2+xy-y2-4x+5y-6因式分解復(fù)習(xí)課知識(shí)要點(diǎn)：多項(xiàng)式-6x2+6xy+3x=-3x(2x-2y-1)二項(xiàng)式a2-b2=(a+b)(a-b)立方差:a3±b3=(a±b)(a2+ab+b2)添項(xiàng):x4+4=x4+4x2+4-4x2=(x2+2+2x)(x2+2-2x)三項(xiàng)式完全平方式:a2±2ab+b2=(a±b)2十字相乘法:a2-29a+100=(a-25)(a-4)拆項(xiàng)法:x3-3x+2=x3-x-2x+2=(x-1)2(x+2)多于三項(xiàng)的多項(xiàng)式分組分解分組后提公因式:ma-mb+na-nb=(a-b)(m+n)分組后運(yùn)用公式:x