Question

ab(a+b)²-(a+b)²+1分解因式

Answer 1

ab(a+b)²-(a+b)²+1
=ab(a+b)^2-(a^2+2ab+b^2)+1
=ab(a+b)^2-(a^2+ab)-(ab+b^2)+1
=ab(a+b)^2-a(a+b)-b(a+b)+1
=a(a+b)[b(a+b)-1]-[b(a+b)-1]
=[b(a+b)-1][a(a+b)-1]
=(ab+b^2-1)(a^2+ab-1)

Answer 2

ab(a+b)²-(a+b)²+1
= a³b+2a²b²+ab³-a²-2ab-b²+1
= a³b+a²(2b²-1)+a(b³-2b)-(b²-1)
= a³b+ a²b²+a²(b²-1)+a(b³-b)-ab-(b²-1)
= [a³b+ a²b²-ab]+[a²(b²-1)+a(b³-b)-(b²-1)]
= ab[a²+ ab-1]+ (b²-1)[a²+ab-1]
= (ab+ b²-1)(a²+ab-1)

Answer 3

（a+b)(ab-1)+1