因式分解：（1）x⁴-x²+8x-16（2）x²y²-y⁴-12xy²+36y²（3）x²-6xy+9y²-3x+9y+2

Question

因式分解：（1）x⁴-x²+8x-16（2）x²y²-y⁴-12xy²+36y²
（3）x²-6xy+9y²-3x+9y+2

Answer 1

解
x⁴-x²+8x-16
=(x²)²-(x²-8x+16)
=(x²)²-(x-4)²
=(x²-x+4)(x²+x-4)
x²y²-y⁴-12xy²+36y²
=y²(x²-12x+36)-y⁴
=y²(x-6)²-y⁴
=y²(x-6-y)(x-6+y)
x²-6xy+9y²-3x+9y+2
=(x-3y)²-3(x-3y)+2
=[(x-3y)-2][(x-3y)-1]
=(x-3y-2)(x-3y-1)