Question

分解因式（1）4(2x2-x+1)(x2-2x+3)-(3x2-3x+4)2 （2）（x+5)^4+(x+3)^4-82

需过程，急急急急急急

Answer 1

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

（2）
（x+5)^4+(x+3)^4-82
= [（x+5)^4-81]+[(x+3)^4-1]
=[(x+5)²+9][(x+5)²-9]+[(x+3)²+1][(x+3)²-1]
=[(x+5)²+9][(x+8)(x+2)]+[(x+3)²+1][(x+4)(x+2)]
=(x+2)[(x²+10x+34)(x+8)+(x²+6x+10)(x+4)]