Ta có:
\(H=4\left(x+5\right)\left(x+6\right)\left(x+10\right)\left(x+12\right)-3x^2\)
\(H=4\left(x+5\right)\left(x+12\right)\left(x+6\right)\left(x+10\right)-3x^2\)
\(H=4\left(x^2+17x+60\right)\left(x^2+16x+60\right)-3x^2\)(1)
Đặt \(t=x^2+16x+60\Rightarrow x^2+17x+60=t+x\), khi đó (1) trở thành:
\(H=4t\left(t+x\right)-3x^2\)
\(H=4t^2+4tx-3x^2\)
\(H=\left(2t\right)^2+2.2t.x+x^2-4x^2\)
\(H=\left(2t+x\right)^2-4x^2\)
\(H=\left(2t+x\right)^2-\left(2x\right)^2\)
\(H=\left(2t+x-2x\right)\left(2t+x+2x\right)\)
\(H=\left(2t-x\right)\left(2t+3x\right)\)
Thay \(t=x^2+16x+60\) vào, ta được:
\(H=\left[2\left(x^2+16x+60\right)-x\right]\left[2\left(x^2+16x+60\right)+3x\right]\)
\(H=\left(2x^2+32x+120-x\right)\left(2x^2+32x+120+3x\right)\)
\(H=\left(2x^2+31x+120\right)\left(2x^2+35x+120\right)\)