分解因式：4b²c²-(b²+c²-a²)² 25（x+y)²-16(x-y)² x²-6x+9

题目

分解因式：4b²c²-(b²+c²-a²)² 25（x+y)²-16(x-y)² x²-6x+9

答案

你好,2铥了幸福
4b²c²-(b²+c²-a²)²
=(2bc)²-(b²+c²-a²)²
=(2bc+b²+c²-a²)(2bc-b²-c²+a²)
=[(b+c)²-a²][a²-(b-c)²]
=(b+c+a)(b+c-a)(a+b-c)(a-b+c)
25(x+y)²-16(x+y)²
=[5(x+y)]²-[4(x+y)]²
=[5(x+y)+4(x+y)][5(x+y)-4(x+y)]
=[9(x+y)][x+y]
=(9x+9y)(x+y)
x²-6x+9
=x²-6x+3²
=(x-3)²