Question

simplify ,
(5m+7n)²+(7m+5n)²​

Answer 1

Answer:

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Answer 2

Using identity

${a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab$

$(5m+7n)²+(7m+5n)² = {(5m + 7n - 7m - 5n)}^{2} + 2(5m + 7n)(7m + 5n) \\ = {( - 2m + 2n)}^{2} + 2 \times (35 {m}^{2} + 25mn + 49mn + 35 {n}^{2} ) \\ = 4 {m}^{2} + 4 {n}^{2} - 2 \times ( 2m)(2n) + 70 {m}^{2} + 148mn + 70 {n}^{2} \\ = 74 {m}^{2} + 74 {n}^{2} + 140mn$