Question

$75(x + {y)}^{2} - 48(x - {y)}^{2}$

Answer 1

$75 {(x + y)}^{2} - 48 {(x - y)}^{2} \\ = 75( {x}^{2} + {y}^{2} + 2xy) - 48( {x}^{2} + {y}^{2} - 2xy) \\ = 75 {x}^{2} + 75 {y}^{2} + 150xy - 48 {x}^{2} - 48 {y}^{2} + 96xy \\ = 27 {x}^{2} + 27 {y}^{2} + 246xy \\ = 3(9 {x}^{2} + 9 {y}^{2} + 82xy)$