Question

tomorrow is my exam please help me to solve this question​

Answer 1

solution 1

$4x {}^{2} + 9y {}^{2} + 16z {}^{2} + 12xy - 24yz - 16xz \\ =( 2x) {}^{2} + (3y) {}^{2} + ( - 4z) {}^{2} + 2(2x)(3y) + 2(3y)( - 4z) + 2( - 4z)(2x) \\ = (2x + 3y - 4z) {}^{2} \\ = (2x + 3y - 4z)(2x + 3y - 4z)$

solution 2

$2x {}^{2} + y {}^{2} + 8z {}^{2} - 2 \sqrt{2} xy + 4 \sqrt{2} yz - 8xz \\ = ( - \sqrt{2} x) {}^{2} + (y ){}^{2} + (2 \sqrt{2} z) {}^{2} + 2( - \sqrt{2} x)(y) + 2(y)(2 \sqrt{2} z) + 2(2 \sqrt{2} z)( - \sqrt{2} x) \\ = ( - \sqrt{2} x + y + 2 \sqrt{2} z) {}^{2} \\ = ( - \sqrt{2} x + y + 2 \sqrt{2} z)( - \sqrt{2} x + y + 2 \sqrt{2} z)$