分解因式(ax+by)2+(bx-ay)2=_.
问题描述:
分解因式(ax+by)2+(bx-ay)2=______.
答
(ax+by)2+(bx-ay)2,
=a2x2+b2y2+2abxy+b2x2+a2y2-2abxy,
=a2x2+b2x2+b2y2+a2y2,
=(a2+b2)x2+(a2+b2)y2,
=(a2+b2)(x2+y2).
故答案为:(a2+b2)(x2+y2).