因式分解：(3x+4y)^2+4(2x-y)(3x+4y)+4(2x-y)^2+2(7x+2y)+1_数学解答

因式分解：(3x+4y)^2+4(2x-y)(3x+4y)+4(2x-y)^2+2(7x+2y)+1

人气：416 ℃　时间：2019-10-17 06:49:34

解答

原式=(3x+4y+4x-2y)^2+2(7x+2y)+1
=(7x+2y)^2+2(7x+2y)+1
=(7x+2y+1)^2(ax+by)^2+(ay-bx)^2+2(ax+by)(ay-bx)+2a(x+y)+2b(y-x)+1原式=(ax+by+ay-bx)^2+2(ax+ay+by-bx)=(ax+ay+by-bx)(ax+ay+by-bx+2)