Question

factorise 2 root 2 a cube + 16 root 2 b cube plus c cube minus 12 ABC

Answer 1

Heres your answer

$2 \sqrt{2} {a}^{3} + 16 \sqrt{2} {b}^{3} + {c}^{3} - 12abc$

Using Identity

${a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - \\ bc - ca)$

Putting values

$= (4 a+ 36 b+ 1c)( 2{a}^{2} + 6 {b}^{2} + {c}^{2} - 12ab - 6bc - 2ca)$

Hope it helps!