因式分解,下列各题.因式分解(1)-27mn+9m²n-18mn(2)9x²-4y²(3)2x²-4x+2(4)x²-y²+2x+2y(5)ax²-bx²+bx-ax+a-b(6)x²-2x-8(7)3x²+2x-1(8)ma-mb+2a-2b(9)3x²-12x³y+12xy²(10)a

Question

因式分解,下列各题.
因式分解
(1)-27mn+9m² n-18mn
(2)9x² -4y²
(3)2x² -4x+2
(4)x² -y² +2x+2y
(5)ax² -bx² +bx-ax+a-b
(6)x² -2x-8
(7)3x² +2x-1
(8)ma-mb+2a-2b
(9)3x² -12x³ y+12xy²
(10)a² -2ab+b² -1

Answer 1

(1)-27mn+9m² n-18mn
=9m²n-45mn
=9mn(m-5)
(2)9x² -4y²
=(3x+2y)(3x-2y)
(3)2x² -4x+2
=2(x²-2x+1)
=2(x-1)²
(4)x² -y² +2x+2y
=(x+y)(x-y)+2(x+y)
=(x+y)(x-y+2)
(5)ax² -bx² +bx-ax+a-b
=x²(a-b)-x(a-b)+(a-b)
=(a-b)(x²-x+1)
(6)x² -2x-8
=(x+2)(x-4)
(7)3x² +2x-1
=(3x-1)(x+1)
(8)ma-mb+2a-2b
=m(a-b)+2（a-b）
=(a-b)(m+2)
(9)3x² -12x³ y+12xy²
=3x(x-4x²y+4y²)
本题可能有误
估计是：3x³-12x²y+12xy²=3x(x²-4xy+4y²)=3x(x-2y)²
(10)a² -2ab+b² -1
=(a-b)²-1
=(a-b+1)(a-b-1)