Question

分解因式： (x+y)(x-y)-(x+y)² 3m(m-n)+6n(n-m) x(x-y)-y(y-x) (x-3)²+（3x-9)

(x+y)(x-y)-(x+y)²
3m(m-n)+6n(n-m)
x(x-y)-y(y-x)
(x-3)²+（3x-9)
急!

Answer 1

解1题
原式=(x+y)[(x-y)-(x+y)]
=(x+y)(x-y-x-y)
=(x+y)×(-2y)
=-2y(x+y)

解2题
原式=3m(m-n)-6n(m-n)
=3(m-n)(m-2n)

解3题
原式=x(x-y)+y(x-y)
=(x-y)(x+y)

解4题
原式=(x-3)²+3(x-3)
=(x-3)[(x-3)+3]
=x(x-3)

Answer 2

(1)(x+y)(x-y)-(x+y)²
=(x＋y)[(x－y)－(x＋y)]
=﹣2y(x＋y)
(2)3m(m-n)+6n(n-m)
=3m(m-n)－6n(m－n)
=(3m－6n)(m－n)
=3(m－2n)(m－n)
(3)x(x-y)-y(y-x)
=x(x-y)＋y(x－y)
=(x＋y)(x－y)
(4)(x-3)²+（3x-9)
=x²－6x＋9＋3x－9
=x²－3x
=x(x－3)