(6x+7)^2(3x+4)(x+1)-6
=(36x²+84x+49)(3x²+7x+4)-6
=(36x²+84x+48+1)(3x²+7x+4)-6
=[12(3x²+7x+4)+1](3x²+7x+4)-6
=12(3x²+7x+4)²+(3x²+7x+4)-6
=[3(3x²+7x+4)-2][3(3x²+7x+4)+3]
=[3(3x²+7x+4)-2][4(3x²+7x+4)+3]
=[9x²+21x+12-2][12x²+28x+16+3]
=(9x²+21x+10)(12x²+28x+19)
=(3x+2)(3x+5)(12x²+28x+19)
原式=(36x²+84x+49)(3x²+7x+4)-6
令a=3x²+7x+4
则36x²+84x+49=12a+1
原式=a(12a+1)-6
=12a²+a-6
=(3a-2)(4a+3)
=(9x²+21x+10)(12x²+28x+19)
=(3x+2)(3x+5)(12x²+28x+19)
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