(X的平方加4X加3)(X的平方加12X加35)加15的因式分解
问题描述：
(X的平方加4X加3)(X的平方加12X加35)加15的因式分解
答
原式=(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=[(x²+8x)+7][(x²+8x)+15]+15
=(x²+8x)²+22(x²+8x)+105+15
=(x²+8x)²+22(x²+8x)+120
=(x²+8x+10)(x²+8x+12)
=(x²+8x+10)(x+2)(x+6)