Question

using algebraic identities solve. (7m -- 8n)2 + (7m + 8n)2​

Answer 1

${\bigstar}$ SOLUTION${\bigstar}$

(7m -- 8n)² + (7m + 8n)2²➜(1)

IDENTITY USED :-

(7m - 8n)²

It is in the form of (a-b)²

$\boxed{\sf{ (a-b)² = a² + b² -2ab }}$

here,

• a = 7m
• b = 8n

➠(7m - 8n)²

➠(7m)² + (8n)² - 2(7m)(8n)

➠ 49m² + 64n² - 112 ➜(2)

IDENTITY USED :-

(7m + 8n)2

It is in the form of (a+b)²

$\boxed{\sf{ (a+b)² = a² + b² +2ab }}$

here,

• a = 7m
• b = 8n

➠(7m + 8n)²

➠(7m)² + (8n)² + 2(7m)(8n)

➠ 49m² + 64n² + 112 ➜(3)

(1)➜(7m -- 8n)2 + (7m + 8n)2

from (2) and (3) ,

➠ 49m² + 64n² - 112 + 49m² + 64n² + 112

➠ 49m² + 64n² + 49m² + 64n²

➠ 2(49m² + 64n²)

➠ $\boxed{\sf{98m² + 128n²}}$

Answer 2

(7m -- 8n)² + (7m + 8n)2²➜(1)

IDENTITY USED :-

(7m - 8n)²

It is in the form of (a-b)²

(a-b)² = a² + b² -2ab }}

(a−b)²=a²+b²−2ab

here,

a = 7m

b = 8n

➠(7m - 8n)²

➠(7m)² + (8n)² - 2(7m)(8n)

➠ 49m² + 64n² - 112 ➜(2)

IDENTITY USED :-

(7m + 8n)2

It is in the form of (a+b)²

{ (a+b)² = a² + b² +2ab }}

(a+b)²=a²+b²+2ab

here,

a = 7m

b = 8n

➠(7m + 8n)²

➠(7m)² + (8n)² + 2(7m)(8n)

➠ 49m² + 64n² + 112 ➜(3)

(1)➜(7m -- 8n)2 + (7m + 8n)2

from (2) and (3) ,

➠ 49m² + 64n² - 112 + 49m² + 64n² + 112

➠ 49m² + 64n² + 49m² + 64n²

➠ 2(49m² + 64n²)

➠(98m²+128n²)