Question

a的3次方-ab的2次方-a+b因式分解 x的4次方-2x的2次方+1 y的2次方-x的2次方+6x-9

（x平方+x）的平方-14（x平方+x）+24

Answer 1

解：
a³-ab²-a+b
=(a³-ab²)-(a-b)
=a(a²-b²)-(a-b)
=a(a-b)(a+b)-(a-b)
=(a-b)[a(a-b)-1]
=(a-b)(a²-ab-1)

x^4-2x²+1
=(x²-1)²
=[(x-1)(x+1)]²
=(x-1)²(x+1)²

y²-x²+6x-9
=y²-(x²-6x+9)
=y²-(x-3)²
=[y+(x-3)][(y-(x-3)]
=(y+x-3)(y-x+3)

(x²+x)²-14(x²+x)+24
=[(x²+x)-2][(x²+x)-12]
=(x²+x-2)(x²+x-12)
=(x-1)(x+2)(x-3)(x+4)