六條maths問題

1) (x - y)^3 - (x - y)^2
=(x-y)^2 [(x-y)-1]
=(x-y)^2 (x-y-1)

2) (2a - b)(x + y) + (b - 2a)(x + y)
=(2a - b)(x + y) - (2a - b)(x + y)
=0

3) ax - bx + cx + cy - by + ay
= x(a-b+c) +y(a-b+c)
=(a-b+c)(x+y)

4) xy+x+y+1
=x(y+1)+(y+1)
=(y+1)(x+1)

5) a^2 - b^2 + ax - bx
=(a-b)(a+b)+x(a-b)
=(a-b)(a+b+x)

6) p^4 - 2p^2q^2 + q^4
=(p^2 - q^2) ^2