Question

将下列各式因式分解

（1）-1+16m的4次方 （2）2a的4次方b的5次方c-2a²b³c
（3）（a-b）的n+2次方-（a-b）的n次方

Answer 1

（1）16m^4-1
=(4m^2+1)(4m^2-1)
=(4m^2+1)(2m+1)(2m-1)

(2)2a^4*b^5*c-2a^2*b^3*c
=2a^2*b^3*c(a^2*b^2-1)
=2a^2*b^3*c(ab+1)(ab-1)

(3)(a-b)^(n+2)-(a-b)^n
=(a-b)^n[(a-b)^2-1]
=(a-b)^n(a-b+1)(a-b-1)

Answer 2

1。-1+16m的4次方
=(4m²+1)(4m²-1)
=(4m²+1)(2m+1)(2m-1)