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几道因式分解(一题10分)(1)a^3-3a^2+3a-1(2)2a^5+4a^4*b+16a^2*b^3+32a*b^4(3)a^2-2a(b-c)+(c-b)^2(4)(x+y)^2-22x-22y+21还有2、4题!

题目详情
几道因式分解(一题10分)
(1)a^3-3a^2+3a-1
(2)2a^5+4a^4*b+16a^2*b^3+32a*b^4
(3)a^2-2a(b-c)+(c-b)^2
(4)(x+y)^2-22x-22y+21
还有2、4题!
▼优质解答
答案和解析
(1)a^3-3a^2+3a-1 =(a-1)^3
(2)2a^5+4a^4*b+16a^2*b^3+32a*b^4
=2a(a^4+2a^3b+8ab^3+16b^4)
=2a(a+2b)(a^3+8b^3)
=2a(a+2b)^2(a^2-12ab^2-6a^2b+4b^2)
(3)a^2-2a(b-c)+(c-b)^2
=(a-b+c)^2
(4)(x+y)^2-22x-22y+21
=(x+y)^2-22(x+y)+21
=(x+y-21)(x+y-1)