Answer
$32+8\sqrt {14}-12\sqrt 2-6\sqrt 7$
Work Step by Step
$(8-\sqrt {18})(4+\sqrt {14})$
=$8(4+\sqrt {14})-\sqrt {18}(4+\sqrt {14})$
=$32+8\sqrt {14}-4\sqrt {18}-(\sqrt {14}\sqrt {18})$
=$32+8\sqrt {14}-4\sqrt {2\times9}-\sqrt {14\times18}$
=$32+8\sqrt {14}-4\sqrt 9\sqrt 2-\sqrt {252}$
=$32+8\sqrt {14}-4(3)\sqrt 2-\sqrt {36\times7}$
=$32+8\sqrt {14}-12\sqrt 2-(\sqrt {36}\times\sqrt 7)$
=$32+8\sqrt {14}-12\sqrt 2-6\sqrt 7$
