Question

Please Solve This NCERT Ouestion With Explanation

Answer 1

i)
$= {4x}^{2} + {9y}^{2} + {16z}^{2} + 12xy - 24yz - 16xz \\ = {(2x)}^{2} + {(3y)}^{2} + {( - 4z)}^{2} + 12xy - 24yz - 16xz \\ = 2 x( {2x}^{} + 3y + 4z) + 3y( {3y}^{} + 2x + 4z) - 4z( - 4z + 2x) \\ = (2x + 3y - 4z)(2x + 3y + 4z)$
ii)
$= {2 x}^{2} + {y}^{2} + {8z}^{2} - 2 \sqrt{2} xy + 4 \sqrt{2} yz - 8xz \\ = {( - \sqrt{ 2}x) }^{2} + {y}^{2} + { (2\sqrt{2}z) }^{2} - 2 \sqrt{2}xy + 4 \sqrt{2} yz - 8xz \\ = - \sqrt{ 2} x( - \sqrt{ 2}x + y + 2 \sqrt{2} z) + y(y + 2 \sqrt{2}z - \sqrt { 2} x) + 2 \sqrt{2}z(2 \sqrt{2} z + y - \sqrt{2} x) \\ = ( - \sqrt{2} x + y + 2 \sqrt{2} )( - \sqrt{2} x - y + 2 \sqrt{2} z)$