Question

(5m-6n)² +(5m+6n)² use identity​

Answer 1

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50m² + 62n²

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${(5m - 6n)}^{2} + {(5m + 6n)}^{2}$

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first solve (5m-6n)² by using identity,

$\blue{ \bold{ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ {(5m - 6n) }^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies {(5m)}^{2} + {(6n)}^{2} -2 \times 5m \times 6n \\ \\ \implies \: 25 {m}^{2} + 36 {n}^{2} - 60mn .........(i)$

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now solve (5m+6n)² by using identity;

$\blue{ \bold{ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ {(5m + 6n)}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \implies {(5m)}^{2} + {(6n)}^{2} + 2 \times 5m \times 6n \: \: \: \: \\ \\ \implies \: 25 {m}^{2} + 36 {n}^{2} + 60mn ..........(ii)$

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we have to find value of (5m-6n)²+ (5m+6n)²

→ (5m-6n)² + (5m+6n)²

now put the value of (5m-6n)² and (5m+6n)² from (i) and (ii)

→ (25m² + 36n² - 60mn) + (25m² + 36n² + 60mn)

→ 25m² + 36n² - 60mn + 25m² + 36n² + 60mn

→ 25m² + 25m² + 36n² + 36n²

→ 50m² + 72n²

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so answer is 50m² + 72n²

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$\bold{ \underline{ \underline \orange{for \: more \: information}}}→$

→ (a + b)² = a² + b² + 2ab

→ (a - b)² = a² + b² - 2ab

→ a² - b² = (a - b)(a + b)

→ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

→ (x + a)(x + b) = x² + (a + b)x + ab

→ (a + b)³ = a³ + b³ + 3ab(a+b)

→ (a - b)³ = a³- b³ - 3ab (a - b)

Answer 2

Answer:

50m² + 62n²

Step-by-step explanation:

(5m−6n)^2 +(5m+6n)^2

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first solve (5m-6n)² by using identity,

(a−b)^2 =a^2 +b^2 −2ab

(5m−6n)^2

⟹(5m)^2 +(6n) ^2 −2×5m×6n

⟹25m^2 +36n^2 −60mn.........(i)

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now solve (5m+6n)² by using identity;

(a+b)^2 =a^2+b^2+2ab

(5m+6n)^2

⟹(5m)^2 +(6n)^2 +2×5m×6n

⟹25m^2+36n^2 +60mn..........(ii)

_________________________

we have to find value of (5m-6n)²+ (5m+6n)²

→ (5m-6n)² + (5m+6n)²

now put the value of (5m-6n)² and (5m+6n)² from (i) and (ii)

→ (25m² + 36n² - 60mn) + (25m² + 36n² + 60mn)

→ 25m² + 36n² - 60mn + 25m² + 36n² + 60mn

→ 25m² + 25m² + 36n² + 36n²

→ 50m² + 72n²

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so answer is 50m² + 72n²

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\bold{ \underline{ \underline \orange{for \: more \: information}}}→

formoreinformation

→

→ (a + b)² = a² + b² + 2ab

→ (a - b)² = a² + b² - 2ab

→ a² - b² = (a - b)(a + b)

→ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

→ (x + a)(x + b) = x² + (a + b)x + ab

→ (a + b)³ = a³ + b³ + 3ab(a+b)

→ (a - b)³ = a³- b³ - 3ab (a - b)