Question

分解因式 分解因式; ⑤a（x-y）-b(y-x）+c ⑥ x(m+n)-y(n+m)+（m+n） ⑦（x+y）²-16（x-y）²

Answer 1

题目⑤后面是不是漏写了c(x-y)

⑤a(x-y)-b(y-x)+c(x-y)
=a(x-y)+b(x-y)+c(x-y)
=(x-y)(a+b+c)

⑥x(m+n)-y(n+m)+（m+n）
=（m+n)(x-y+1)

⑦（x+y）²-16（x-y）²
=[x+y+4(x-y)][x+y-4(x-y)]
=(x+y+4x-4y)(x+y-4x+4y)
=(5x-3y)(5y-3x)

Answer 2

⑤a（x-y）-b(y-x）+c
=(a+b)x-(a+b)y+c
=(a+b)(x-y)+c
⑥ x(m+n)-y(n+m)+（m+n）
=(x-y+1)m+(x-y+1)n
=(x-y+1)(m+n)

Answer 3

⑤
a(x-y)+b(y-x)+c(x-y)
=a(x-y)-b(x-y)+c(x-y)
=(x-y)(a-b+c)
⑥
x(m+n)-y(n+m)+(m+n)
=x(m+n)-y(m+n)+(m+n)
=(m+n)(x-y+1)
⑦（x+y）²-16（x-y）²
=[x+y+4(x-y)][x+y-4(x-y)]
=(x+y+4x-4y)(x+y-4x+4y)
=(5x-3y)(5y-3x)