19. \( \left(x^{2}+\frac{3}{2}\right)\left(x^{2}-\frac{3}{2}\right) \)

To factor \( \left(x^{2}+\frac{3}{2}\right)\left(x^{2}-\frac{3}{2}\right) \), we can recognize that this expression is in the form of a difference of squares. The formula for the difference of squares is \( a^2 - b^2 = (a+b)(a-b) \). Here, we can let \( a = x^2 \) and \( b = \frac{3}{2} \). Thus, we have: \[ \left(x^{2}\right)^{2} - \left(\frac{3}{2}\right)^{2} = x^{4} - \frac{9}{4}. \] So, the factored form of the original expression is: \[ x^{4} - \frac{9}{4}. \] This can be rewritten as: \[ \left(x^2 + \frac{3}{2}\right)\left(x^2 - \frac{3}{2}\right) = x^{4} - \frac{9}{4}. \]