1、設x²-4x=y
則(x²-4x-12)(x²-4x+3)+56
=(y-12)(y+3)+56
=y²-9y+20
=(y-4)(y-5)
=(x²-4x-4)(x²-4x-5)
=(x+1)(x-5)(x²-4x-4)
2、(x-1)(x+2)(x-3)(x-6)+56
=[(x+2)(x-6)][(x-1)(x-3)]+56
=(x²-4x-12)(x²-4x+3)+56
之后的過程就和第1題一樣,
結果是=(x+1)(x-5)(x²-4x-4)
3、(x²-7x+6)(x²-x-6)+56
=(x-6)(x-1)(x+2)(x-3)
=(x-1)(x+2)(x-3)(x-6)+56
之后的過程就和第2題一樣,
結果是=(x+1)(x-5)(x²-4x-4)
4、(x+y)⁴-(x-y)⁴
=[(x+y)²]-[(x-y)²]²
=[(x+y)²+(x-y)²][(x+y)²-(x-y)²]
=(x²+2xy+y²+x²-2xy+y²){[(x+y)+(x-y)][(x+y)-(x-y)]}
=[2(x²+y²)]·(2x)·(2y)
=8xy(x²+y²)
5、ab(c²+d²)+cd(a²+b²)
=abc²+abd²+a²cd+b²cd
=ac·bc+ad·bd+ac·ad+bc·bd
=ac(bc+ad)+bd(ad+bc)
=(ac+bd)(ad+bc)
6、3a²x²-15a²xy-42a²y²
=3a²·x²-3a²·5xy-3a²·14y²
=3a(x²-5xy-14y²)
=3a²(x+2y)(x-7y)