作业帮在线求助完全平方公式因式分解
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/27 12:11:50
在线求助完全平方公式因式分解
(1)-a²-1+2a
(2)2x²y-x²-xy²
(3)4x²-20x+25
(4)(x²+1)²-4x²
(5)(2x-y)²-2(2x-y)+1
(6)(x+y)²-2(x²-y²)+(x-y)²
(1)-a²-1+2a
(2)2x²y-x²-xy²
(3)4x²-20x+25
(4)(x²+1)²-4x²
(5)(2x-y)²-2(2x-y)+1
(6)(x+y)²-2(x²-y²)+(x-y)²
(1)-a²-1+2a
=-(a^2-2a+1)
=-(a-1)^2
(2)2x²y-x²-xy²
=-x(x-2xy+y^2)
(3)4x²-20x+25
=(2x-5)^2
(4)(x²+1)²-4x²
=(x^2+1+2x)(x^2+1-2x)
=(x+1)^2(x-1)^2
(5)(2x-y)²-2(2x-y)+1
=(2x-y-1)^2
(6)(x+y)²-2(x²-y²)+(x-y)²
=(x+y)^2-2(x+y)(x-y)+(x-y)^2
=(x+y-x+y)^2
=4y^2
=-(a^2-2a+1)
=-(a-1)^2
(2)2x²y-x²-xy²
=-x(x-2xy+y^2)
(3)4x²-20x+25
=(2x-5)^2
(4)(x²+1)²-4x²
=(x^2+1+2x)(x^2+1-2x)
=(x+1)^2(x-1)^2
(5)(2x-y)²-2(2x-y)+1
=(2x-y-1)^2
(6)(x+y)²-2(x²-y²)+(x-y)²
=(x+y)^2-2(x+y)(x-y)+(x-y)^2
=(x+y-x+y)^2
=4y^2