Question

factorise 3x2 + 16y2 + 8z2 + 8√3 xy -16√3 yz - 4√6 zx

Answer 1

$compare \: the \: equation \: with \: identity \\ {(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2xy + 2yz + 2xz \\ = ( { \sqrt{3}x) }^{2} + ( {4y)}^{2} + ( { - 2 \sqrt{2} z)}^{2} \\ + 2( \sqrt{ 3}x)(4y) + 2(4y)( - 2 \sqrt{2}z) + 2( \sqrt{3} x)( - 2 \sqrt{2} z) \\ = ( { \sqrt{3} x + 4y - 2 \sqrt{2}z)}^{2} \\ = ( \sqrt{3}x + 4y - 2 \sqrt{2} z)( \sqrt{3}x + 4y - 2 \sqrt{2}z)$