\(4\left(x+5\right)\left(x+6\right)\left(x+10\right)\left(x+12\right)-3x^2\)
\(=2\left(x+5\right)\left(x+12\right).2\left(x+6\right)\left(x+10\right)-3x^2\)
\(=\left(2x^2+34x+120\right).\left(2x^2+32x+120\right)-3x^2\)
Đặt: \(a=2x^2+33x+120\) , ta có:
\(\left(a+x\right)\left(a-x\right)-3x^2\)
\(=a^2-x^2-3x^2\)
\(=a^2-4x^2\)
\(=\left(a-2x\right)\left(a+2x\right)\)
Thay \(a=2x^2+33x+120\) ta có:
\(\left(2x^2+33x+120-2x\right)\left(2x^2+33x+120+2x\right)\)
\(=\left(2x^2+31x+120\right)\left(2x^2+35x+120\right)\)
\(=\left(2x^2+16x+15x+120\right)\left(2x^2+35x+120\right)\)
\(=\left[2x\left(x+8\right)+15\left(x+18\right)\right]\left(2x^2+35x+120\right)\)
\(=\left(x+8\right)\left(2x+15\right)\left(2x^2+35x+120\right)\)