因式分解（十字相乘法）6a^4-5a^3-4a^24a^6-37a^4b^2+9a^2b^4(x^2-3)^2-4x^2(3x^2+2x+1)^2-(2x^2+3x+3)^2

Question

因式分解（十字相乘法）
6a^4-5a^3-4a^2
4a^6-37a^4b^2+9a^2b^4
(x^2-3)^2-4x^2
(3x^2+2x+1)^2-(2x^2+3x+3)^2

Answer 1

6a^4-5a^3-4a^2
=a^2(6a^2-5a-4)
=a^2(3a-4)(2a+1)
4a^6-37a^4b^2+9a^2b^4
=a^2(4a^4-37a^2b^2+9b^4)
=a^2(4a^2-b^2)(a^2-9b^2)
=a^2(2a+b)(2a-b)(a+3b)(a-3b)
(x^2-3)^2-4x^2
=(x^2-3-2x)(x^2-3+2x)
=(x-3)(x+1)(x-1)(x+3)
(3x^2+2x+1)^2-(2x^2+3x+3)^2
=(3x^2+2x+1+2x^2+3x+3)(3x^2+2x+1-2x^2-3x-3)
=(5x^2+5x+4)(x^2-x-2)
=(5x^2+5x+4)(x-2)(x+1)