Question

सरळरूप द्या: (x -2y + 3)² + (x + 2y -3)²

Answer 1

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca$

${(x - 2y + 3)}^{2} = {x}^{2} + {( - 2y)}^{2} + {(3)}^{2} + 2(x)( - 2y) + 2( - 2y)(3) + 2(3)(x) \\ \\ = {x}^{2} + 4 {y}^{2} + 9 - 4xy - 12y + 6x$
${(x + 2y - 3)}^{2} = {x}^{2} + {( 2y)}^{2} + {( - 3)}^{2} + 2(x)( 2y) + 2( 2y)( - 3) + 2( - 3)(x) \\ \\ = {x}^{2} + 4 {y}^{2} + 9 + 4xy - 12y - 6x$
➡️
${(x - 2y + 3)}^{2} + {(x + 2y - 3)}^{2} \\ \\ = {x}^{2} + 4 {y}^{2} + 9 - 4xy - 12y + 6x + {x}^{2} + 4 {y}^{2} + 9 + 4xy - 12y - 6x \\ \\ =2 {x}^{2} + 8 {y}^{2} + 18 - 24y$