作业帮几道因式分解（一题10分）
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/06/01 09:22:27
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！
（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！
（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)
(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)