求解快10.3x^2y^3,2x^2y,-5x^3y^3z的公因式是____.16.若（a+m)(a-1)=a^2-3a+n,则m+n的值为_____.20.已知a^2+b^2=1,x^2+y^2=1,求（ax+by)^2+(bx-ay)^2
问题描述：
求解快10.3x^2y^3,2x^2y,-5x^3y^3z的公因式是____.
16.若（a+m)(a-1)=a^2-3a+n,则m+n的值为_____.
20.已知a^2+b^2=1,x^2+y^2=1,求（ax+by)^2+(bx-ay)^2
答
10. 3x²y³,2x²y,-5x³y³z的公因式是x²y
16. (a+m)(a-1)=a²+(m-1)a-m=a²-3a+n
=>m=-n
=>m+n=0
20. (ax+by)²+(bx-ay)²
=a²x²+2abxy+b²y²+b²x²-2abxy+a²y²
=a²(x²+y²)+b²(x²+y²)
=a²+b²
=1
答
16.0
17.1
答
3x^2y^3,2x^2y,-5x^3y^3z的公因式是 x^2y
若（a+m)(a-1)=a^2-3a+n,则m+n的值为 0
a^2+(m-1)a-m=a^2-3a+n
得：m-1=-3 即：m=-2
-m=n 得：n=2
已知a^2+b^2=1,x^2+y^2=1,求（ax+by)^2+(bx-ay)^2
（ax+by)^2+(bx-ay)^2
=a^2x^2+2axby+b^2y^2+b^2x^2-2bxay+a^2y^2
=a^2(x^2+y^2)+b^2(x^2+y^2)
=(a^2+b^2)(x^2+y^2)
=1