因式分解(m-2n)四次方-(m-2n)的平方-129x的平方+18x+9-y的平方-2y-1

Question

因式分解
(m-2n)四次方-(m-2n)的平方-12
9x的平方+18x+9-y的平方-2y-1

Answer 1

(m-2n)^4-(m-2n)^2-12
=[(m-2n)^2]^2-(m-2n)^2-12
=[(m-2n)^2+3][(m-2n)^2-4]
=(m-2n-2)(m-2n+2)[(m-2n)^2+3]
9x^2+18x+9-y^2-2y-1
=(3x+3)^2-(y+1)^2
=(3x+3+y+1)(3x+3-y-1)
=(3x+y+4)(3x-y+2)