Question

把下列各式分解因式

⑴3ax-3ay+xy-y²
⑵8x三次方+4x²-2x-1
⑶5x²-15x+2xy-6y
⑷4xy+1-4x²-y²

Answer 1

⑴
3ax-3ay+xy-y²
=3a(x-y)+y(x-y)
=(3a+y)(x-y)
⑵
8x³+4x²-2x-1
=(8x³-2x)+(4x²-1)
=2x(4x²-1)+(4x²-1)
=(4x²-1)(2x+1)
=(2x+1)(2x-1)(2x+1)
=(2x+1)²(2x-1)
⑶
5x²-15x+2xy-6y
=5x(x-3)+2y(x-3)
=(5x+2y)(x-3)
⑷
4xy+1-4x²-y²
=1-(y²-4xy+4x²)
=1-(y-2x)²
=(1+y-2x)(1-y+2x)