using algebraic identities solve. (7m -- 8n)2 + (7m + 8n)2
Answers
SOLUTION
(7m -- 8n)² + (7m + 8n)2²➜(1)
IDENTITY USED :-
(7m - 8n)²
It is in the form of (a-b)²
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
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)
➠
(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)