把9(x-y)2+12(x2-y2)+4(x+y)2因式分解是(  ) A.(3x-2y)(3x+2y) B.(5x+y)2 C.(5x-y)2 D.(5x-2y)2

问题描述:

把9(x-y)2+12(x2-y2)+4(x+y)2因式分解是(  )
A. (3x-2y)(3x+2y)
B. (5x+y)2
C. (5x-y)2
D. (5x-2y)2

9(x-y)2+12(x2-y2)+4(x+y)2
=[3(x-y)]2+12(x+y)(x-y)+[2(x+y)]2
=[3(x+y)+2(x-y)]2
=(5x-y)2
故选C.