\(x^4+81\)
\(=x^4+81+18x^2-18x^2\)
\(=\left[\left(x^2\right)^2+2.x^2.9+9^2\right]-18x^2\)
\(=\left(x^2+9\right)^2-\left(\sqrt{18}x\right)^2\)
\(=\left(x^2+9-\sqrt{18}x\right)\left(x^2+9+\sqrt{18}x\right)\)
\(x^4+81\)
\(=x^4+81+16x^2-16x^2\)
\(=\left(x^2+9\right)^2-16x^2\)
\(=\left(x^2+9+4x\right)\left(x^2+9-4x\right)\)
\(x^4+81\\ =x^4+81-18x^2+18x^2\\ =\left(x^4+18x^2+81\right)-18x^2\\ =\left(x^2+9\right)^2-\left(\sqrt{18}x\right)^2\\ =\left(x^2+9+\sqrt{18x}\right)\left(x^2+9-\sqrt{18x}\right)\)
x4+81
=> x4+18x2+81-18x2
=>(x4+18x2+81)-18x2
=> (x2+9)2-18x2
=> (x2+9-\(\sqrt{18x}\))(x2+9+\(\sqrt{18x}\) )
