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)

不懂可以追问！

Answer 2

(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)
(10)a² -2ab+b² -1
=(a-b)²-1
=(a-b+1)(a-b-1)

不懂可以追问！