\(=\left(36x^2+60x+25\right)\left(3x^2+5x+2\right)-6\)
\(=\left[12\left(3x^2+5x+2\right)+1\right]\left(3x^2+5x+2\right)-6\)
\(=12\left(3x^2+5x+2\right)^2+\left(3x^2+5x+2\right)-6\)
\(=\left[3\left(3x^2+5x+2\right)-2\right]\left[4\left(3x^2+5x+2\right)+3\right]\)
\(=\left(9x^2+15x+4\right)\left(12x^2+20x+11\right)\)
\(=\left(3x+1\right)\left(3x+4\right)\left(12x^2+20x+11\right)\)
Lời giải:
\((6x+5)^2(3x+2)(x+1)-6\)
\(=(36x^2+60x+25)(3x^2+5x+2)-6\)
\(=[12(3x^2+5x+2)+1](3x^2+5x+2)-6\)
\(=(12a+1)a-6\) (đặt \(3x^2+5x+2=a)\)
\(=4a(3a-2)+3(3a-2)=(4a+3)(3a-2)\)
\(=(12x^2+20x+11)(9x^2+15x+4)\)
\(=(12x^2+20x+11)[3x(3x+1)+4(3x+1)]\)
\(=(12x^2+20x+11)(3x+4)(3x+1)\)
