分解因式1.(x+y)²-(x+y)(x-y)2.(x+y)²-10(x+y)+253.(1-a²)(1-b²)-4ab4.(x+1)(x+2)(x+3)(x+4)+1

Question

分解因式
1.(x+y)²-(x+y)(x-y)
2.(x+y)²-10(x+y)+25
3.(1-a²)(1-b²)-4ab
4.(x+1)(x+2)(x+3)(x+4)+1

Answer 1

1.(x+y)^2-(x+y)(x-y)
=(x+y)[(x+y)-(x-y)]
=2y(x+y)
2.(x+y)^2-10(x+y)+25
=(x+y)^2-10(x+y)+5^2
=(x+y-5)^2
3.(1-a^2)(1-b^2)-4ab
=1-a^2-b^2+a^2b^2-4ab
=(1-2ab+a^2b^2)-(a^2-2ab+b^2)
=(1-ab)^2-(a-b)^2
=[(1-ab)+(a-b)][(1-ab)-(a-b)]
=(1+a-b-ab)(1-a+b-ab)
4.(x+1)(x+2)(x+3)(x+4)+1
=(x+1)(x+4)(x+2)(x+3)+1
=(x^2+5x+4)(x^2+5x+6)+1
=(x^2+5x)^2+10(x^2+5x)+24+1
=(x^2+5x)^2+10(x^2+5x)+5^2
=(x^2+5x+5)^2
------------这一下子答了四道题呀.