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

Question

(3)(a+b)(a-b)+c(2b-c)
(2)(ab+1)²-(a+b)²

Answer 1

(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)

Answer 2

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)

Answer 3

36x^n+12x^(n+1)+x^(n+2)
=36x^n+12x^n*x+x^2*x^n
=x^n(36+12x+x^2)
=x^n(x+6)^2

(ab+1)^2-(a+b)^2
=(ab+1-a-b)(ab+1+a+b)
=(a-1)(b-1)(a+1)(b+1)

(a+b)(a-b)+c(2b-c)
=a^2-b^2+2bc-c^2
=a^2-(b^2-2bc+c^2)
=a^2-(b-c)^2
=[a-(b-c)][a+(b-c)]
=(a-b+c)(a+b-c)

Answer 4

(a+b)(a-b)+c(2b-c)
=a^2-b^2+2bc-c^2
=a^2-(b-c)^2
=-(b-c+a)(b-c-a)