Question

因式分解 要过程

x²y+xy²-xy
a²-b²+a+b
25(a+b）²-（a+b)²
(x²+y²）²-4x²y²
8a³-2a（a+1）²

Answer 1

x²y+xy²-xy
=xy(x+y+1)
a²-b²+a+b
=(a+b)(a-b)+(a+b)
=(a+b)(a-b+1)
25(a+b）²-（a+b)²
=24(a+b)²
(x²+y²）²-4x²y²
=(x²+y²-2xy)(x²+y²+2xy)
=(x-y)²(x+y)²

8a³-2a（a+1）²
=2a(4a²-(a+1)²)
=2a(2a+a+1)(2a-a-1)
=-2a(3a+1)(a-1)

Answer 2

x²y+xy²-xy=xy(x+y-1)
a²-b²+a+b=(a+b)(a-b)+(a+b)=(a+b)(a-b+1)
25(a+b）²-（a+b)²=24(a+b)²
(x²+y²）²-4x²y²=x^4+2x^2y^2+y^4-4x²y²=x^4-2x^2y^2+y^4=(x²-y²）²
8a³-2a（a+1）²=2a[4a^2-(a+1)^2]=2a(2a+a+1)(2a-a-1)=2a(3a+1)(a-1)

Answer 3

x²y+xy²-xy=xy(x+y-1)
a²-b²+a+b=(a+b)(a-b)+(a+b)=(a+b)(a-b+1)
25(a+b）²-（a+b)²=(25-1)(a+b）²=24(a+b）²
(x²+y²）²-4x²y²=x^4+2x²y²+y^4-4x²y²=x^4-2x²y²+y^4=(x²-y²）²
8a³-2a（a+1）²=8a³-2a(a²+2a+1)=8a³-2a³-4a²-2a=2a(3a²-2a-1)=2a(3a+1)(a-1)