Question

math question please help this question

Answer 1

$8x { }^{2} + y {}^{2} + 27 - 4 \sqrt{2} xy - 6 \sqrt{3} y + 12 \sqrt{6} x$
This can be factorised using this algebraic identity:-
$(a + b+ c) {}^{2} = {a}^{2} + {b}^{2} + {c}^{2} \\ + 2ab + 2 bc+ 2ca$
So,
$= (2 \sqrt{2} x) {}^{2} + ( - y) {}^{2} +(3 \sqrt{3} ) {}^{2} + 2 \times 2 \sqrt{2} x \times( - y) \\ + 2 \times ( - y) \times 3 \sqrt{3} + 2 \times 3 \sqrt{3} \times 2 \sqrt{2} x \\ = (2 \sqrt{2} x - y + 3\sqrt{3} ) {}^{2} \\ = (2 \sqrt{2} x - y + 3 \sqrt{3} )(2 \sqrt{2} x - y + 3 \sqrt{3} )$



-------Hope this will help you-----