Question

3(a-b)³+(b-a)² ,分解因式

x(y-x)²(a-b)+(x-y)³(b-a)
已知m²+n²=5,x²+y²=41,求多项式(mx+ny)²+(nx-my)²的值

Answer 1

=3(a-b)³+(a-b)²
=(a-b)²(3a-3b+1)

追问

x(y-x)²(a-b)+(x-y)³(b-a)

追答

=x(x-y)²(a-b)-(x-y)³(a-b)
=(x-y)²(a-b)[x-(x-y)]
=y(x-y)²(a-b)

追问

已知m²+n²=5,x²+y²=41,求多项式(mx+ny)²+(nx-my)²的值

追答

不能没完没了的追问
(mx+ny)²+(nx-my)²
=m²x²+2mnxy+n²y²+n²x²-2mnxy+m²y²
=(m²+n²)(x²+y²)
=5×41
=205