（1）4（x²+3x+1）²-（x²+x-4）²-(x²+5x+6)²）（2）a^5+a^4+1(3)ax^4-9x²+6x-1(4)(x²+3x+4)(x²+3x+5)-6(5)a²b²-a²-b²

Question

（1）4（x²+3x+1）²-（x²+x-4）²-(x²+5x+6)²）
（2）a^5+a^4+1
(3)ax^4-9x²+6x-1
(4)(x²+3x+4)(x²+3x+5)-6
(5)a²b²-a²-b²

Answer 1

（1）4（x²+3x+1）²-（x²+x-4）²-(x²+5x+6)²
=[2(x²+3x+1)-(x²+x-4)][2(x²+3x+1)+(x²+x-4)]-(x²+5x+6)²
=[2x²+6x+2-x²-x+4][2x²+6x+2+x²+x-4]-(x²+5x+6)²
=[x²+5x+6][3x²+7x-2]-(x²+5x+6)²
=(x²+5x+6)[(3x²+7x-2)-(x²+5x+6)]
=(x²+5x+6)(3x²+7x-2-x²-5x-6)
=(x²+5x+6)(2x²+2x-8)
=(x+2)(x+3)[2(x²+x-4)]
=2(x+2)(x+3)(x²+x-4)
（2）a^5+a^4+1
=a^5+a^4+a^3-a^3+1
=a^3(a^2+a+1)-(a^3-1)
=a^3(a^2+a+1)-(a-1)(a^2+a+1)
=(a^3-a+1)(a^2+a+1)
(3)x^4-9x²+6x-1
=x^4-(9x²-6x+1)
=x^4-(3x-1)^2
=(x^2-3x+1)(x^2+3x-1)
(4)(x²+3x+4)(x²+3x+5)-6
=(x²+3x+4)[(x²+3x+4)+1]-6
=(x²+3x+4)²+(x²+3x+4)-6
=(x²+3x+4+3)(x²+3x+4-2)
=(x²+3x+7)(x²+3x+2)
=(x²+3x+7)(x+1)(x+2)
(5)a²b²-a²-b²+1
=a²(b²-1)-(b²-1)
=(a²-1)(b²-1)
=(a-1)(a+1)(b-1)(b+1)