(4x-1)^3+(2x-3)^3+6(3x-2)(4x-1)(2x-3)
= [(4x-1)^3+(2x-3)^3] +6(3x-2)(4x-1)(2x-3)
= [(4x-1)+(2x-3)][(4x-1)^2+(4x-1)(2x-3)+(2x-3)^2] + (18x - 12 )(4x-1)(2x-3)
=[(4x-1)+(2x-3)] {[(4x)^2 - 2.4x.1+1^2] + (8x^2 - 12x - 2x + 3) + [(2x)^2 - 2.2x.3 + 3^2]} + (72x^2 - 18x - 48x + 12)(2x-3)
=(4x-1+2x-3) [(16x^2 - 8x+1) + (8x^2 - 12x - 2x + 3) + ( 4x^2 - 12x + 9 )] + (144x^3 - 36x^2 - 96x^2 + 24x - 216x^2 + 54x + 144x - 36)
=(6x-4) (16x^2 - 8x+1+8x^2 - 12x - 2x + 3+4x^2 - 12x + 9)+ (144x^3 - 36x^2 - 96x^2 + 24x - 216x^2 + 54x + 144x - 36)
=(6x-4)[(16x^2+8x^2+4x^2) + ( - 8x - 12x - 2x - 12x)+(1 + 3+ 9)]+ [144x^3 + (- 36x^2 - 96x^2 - 216x^2) + ( 24x + 54x+ 144x) - 36 ]
=(6x-4) (28x^2-34x+13) +( 144x^3 -348x^2+222x-36)
=(168x^3-204x^2+78x-112x^2+136x-52)+( 144x^3 -348x^2+222x-36)
=(168x^3-316x^2+214x-52)+( 144x^3 -348x^2+222x-36)
=168x^3-316x^2+214x-52+144x^3 -348x^2+222x-36
=(168x^3+144x^3)+(-316x^2-348x^2)+(214x+222x)+(-52-36)
=312x^3-664x^2+436x-88
=4(78x^3-166x^2+109x-22