a) x16+1 = (x16+2x8+1) - 2x8 = (x8+1)2-2x8 = \(\left(x^8-\sqrt{2}x^4+1\right)\left(x^8+\sqrt{2}x^4+1\right)\)
b) 81x4+144 = (81x4+216x2+144)-216x2 = (9x2+12)2-216x2
\(=\left(9x^2-6\sqrt{6}x+12\right)\left(9x^2+6\sqrt{6}x+12\right)\)
c) \(4x^4+9=\left(4x^4+12x^2+9\right)-12x^2=\left(2x^2+3\right)^2-12x^2\)
\(=\left(2x^2-2\sqrt{3}x+3\right)\left(2x^2+2\sqrt{3}x+3\right)\)
d) \(16x^4y^4+1=\left(16x^4y^4+4x^2y^2+1\right)-4x^2y^2=\left(4x^2y^2+1\right)^2-4x^2y^2=\left(4x^2y^2-2xy+1\right)\left(4x^2y^2+2xy+1\right)\)
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