Let θ be the angle between the vectors → a and → b , where | → a |...

${\left|\left(\overset{\to}{a} - \overset{\to}{b}\right) \times \left(\overset{\to}{a} + \overset{\to}{b}\right)\right|}^{2} + 4{\left(\overset{\to}{a} \cdot \overset{\to}{b}\right)}^{2}$

$= {\left|\overset{\to}{a} \times \overset{\to}{a} + \overset{\to}{a} \times \overset{\to}{b} - \overset{\to}{b} \times \overset{\to}{a} - \overset{\to}{b} \times \overset{\to}{b}\right|}^{2} + 4{\left(\overset{\to}{a} ⋅ \overset{\to}{b}\right)}^{2}$

$= 4\left[{\left|\overset{\to}{a} \times \overset{\to}{b}\right|}^{2} + {\left(\overset{\to}{a} \cdot \overset{\to}{b}\right)}^{2}\right] = 4{\left|\overset{\to}{a}\right|}^{2}{\left|\overset{\to}{b}\right|}^{2} = 4 \times 9 \times 16 = 576$