Simplify frac 10 sqrt 3 sqrt 5 - sqrt 15 2 - WAEC Mathematics 2016 Question

Note that (\frac{10\sqrt{3}}{\sqrt{5}} = \frac{10\sqrt{3}}{\sqrt{5}} \times - \frac{\sqrt{5}}{\sqrt{5}})

= (\frac{10\sqrt{15}}{\sqrt{5}} = 2\sqrt{15})

hence, ((\frac{10\sqrt{3}}{\sqrt{5}} - \sqrt{15}))² = ((2\sqrt{15} - \sqrt{15}))²

= ((2\sqrt{15} - \sqrt{15}))((2\sqrt{15} - \sqrt{15}))

= 4(\sqrt{15 \times 15} - 2\sqrt{15 \times 15} - 2\sqrt{15 x 15} + \sqrt{15 \times 15})

= 4 x 15 - 2 x 15 - 2 x 15 + 15

= 60 - 30 - 30 + 15

= 15