因式分解：（1）36x的n次方+12x的n+1次方+x的n+2次方 （2）（ab+1)²－(a+b)²(3)(a+b)(a-b)+c(2b-c)(2)(ab+1)²-(a+b)²
问题描述：
因式分解：（1）36x的n次方+12x的n+1次方+x的n+2次方 （2）（ab+1)²－(a+b)²
(3)(a+b)(a-b)+c(2b-c)
(2)(ab+1)²-(a+b)²
答
36x的n次方+12x的n+1次方+x的n+2次方
=x的n次方(36+12x+x²)
=x的n次方(6+x)²
（ab+1)²－(a+b)²
=(ab+1+a+b)(ab+1-a-b)
=[a(b+1)+(b+1)][a(b-1)-(b-1)]
=(a+1)(b+1)(a-1)(b-1)
(a+b)(a-b)+c(2b-c)
=a²-b²+2bc-c²
=a²-(b-c)²
=(a+b-c)(a-b+c)
答
(1)36x^n+12x^(n+1)+x^(n+2)
=x^n(36+12x+x²)
=x^n(6+x)²
(2)(ab+1)²-(a+b)²
=[(ab+1)+(a+b)][(ab+1)-(a+b)]
=(ab+1+a+b)(ab+1-a-b)
=[a(b+1)+(b+1)][a(b-1)-(b-1)]
=(a+1)(b+1)(a-1)(b-1)
=(a²-1)(b²-1)
(3)(a+b)(a-b)+c(2b-c)
=a²-b²+2bc-c²
=a²-(b²-2bc+c²)
=a²-(b-c)²
=[a+(b-c)][a-(b-c)]
=(a+b-c)(a-b+c)