Question

因式分解：(1)(a-b)^n+2-(a-b)n (2)4+4xy-y^2-4x^2

Answer 1

（1）（a－b）^n＋2－（a－b）^n
=(a－b)^n (a－b)²－（a－b）^n
=（a－b）^n[(a－b)²－1]
=(a－b)^n(a－b＋1)(a－b－1)
(2)原式为：4＋4xy－y²－4x²
=4－(4x²－4xy＋y²)
=2²－[(2x)²－2×2xy＋y²]
=2²－(2x－y)²
=(2＋2x－y)(2－2x＋y)

Answer 2

(1) (a-b)^(n+2)-(a-b)^n=(a-b)^n[(a-b)^2-1]
=(a-b)^n[(a-b)-1][(a-b)+1]
=(a-b)^n(a-b-1)(a-b+1)
(2) 4+4xy-y^2-4x^2
=4-(4x^2-4xy+y^2)
=4-(2x-y)^2
=[2-(2x-y)][2+(2x-y)]
=(2x-y+2)(-2x+y+2)