Question

simplify (7m-5n)(7m+5n)+(5m+7n)(5m+7n)​

Answer 1

(7m -5n ×7m+5n)+(5m+7n×5m +7n)

42m square -25nsquare+25m square +70mn+42n square

Answer=67m square +70mn+17 n square

Answer 2

Given : The given algebraic expression is, (7m-5n)(7m+5n)+(5m+7n)(5m+7n)

To find : The simplification of the given algebraic expression.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to simplify the given algebraic expression)

Here, we will be using algebraic identities to simplify the given algebraic expression. (usage of identities will make the calculations easier)

So,

= (7m-5n) (7m+5n) + (5m+7n) (5m+7n)

= [(7m-5n) (7m+5n)] + [(5m+7n) (5m+7n)]

= [(7m+5m) (7m-5n)] + (5m+7n)²

= [(7m)²-(5n)²] + [(5m)² + (2 × 5m × 7n) + (7n)²]

= (49m²-25n²) + (25m²+70mn+49n²)

= 49m²-25n²+25m²+70mn+49n²

= 74m²+70mn+24n²

= 2(37m²+35mn+12n²)

(This cannot be further simplified. That's why, this will be considered as the final result.)

Used identity :

• (a+b) (a-b) = a²-b²
• (a+b)² = a²+2ab+b²

Hence, the answer to the simplification is 2(37m²+35mn+12n²)