Question

सरळरूप द्या: (3k -4r -2m)² - (3k + 4r - 2m)²

Answer 1

सरळरूप:

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca$
${(3k - 4r - 2m)}^{2} = \\ \\ {(3k)}^{2} + {( - 4r)}^{2} + {( - 2m)}^{2} + \\ \\ 2(3k)( - 4r) + 2( - 4r)( - 2m) + 2( - 2m)(3k)\\ \\ = 9 {k}^{2} + 16 {r}^{2} + 4 {m}^{2} - 24kr + 16rm - 12mk$

${(3k + 4r - 2m)}^{2} = \\ \\ {(3k)}^{2} + {( 4r)}^{2} + {( - 2m)}^{2} + \\ \\ 2(3k)( 4r) + 2( 4r)( - 2m) + 2( - 2m)(3k)\\ \\ = 9 {k}^{2} + 16 {r}^{2} + 4 {m}^{2} + 24kr - 16rm - 12mk$
➡️${(3k - 4r - 2m)}^{2} - {(3k + 4r - 2m)}^{2} \\ \\ = 9 {k}^{2} + 16 {r}^{2} + 4 {m}^{2} - 24kr + 16rm - 12mk \\ \\ - (9 {k}^{2} + 16 {r}^{2} + 4 {m}^{2} + 24kr - 16rm - 12mk) \\ \\ = - 48kr + 32rm$