Question

simplify (7m-8n)² +(7m+8n)² ​

Answer 1

Clarification:

Here, we have to simply the given expression :

• (7m-8n)² +(7m+8n)²

As, we know that " (a+b)² = a² + 2ab + b² & (a-b)² = a² - 2ab + b² ", we'll apply these two identities and then we'll perform addition in order to get our answer.

To simplify:

• (7m-8n)² +(7m+8n)²

Identities to be used:

• (a+b)² = a² + 2ab + b²

• (a-b)² = a² - 2ab + b²

Solution:

→ (7m-8n)² +(7m+8n)²

By using (a+b)² = a² + 2ab + b² & (a-b)² = a² - 2ab + b² identities :

→ [ (7m)² - (2 × 7m × 2n) + (8n)² ] + [ (7m)² + (2 × 7m × 2n) + (8n)² ]

Removing brackets by performing multiplication.

→ ( 49m² - 112mn + 64n² ) + ( 49m² + 112mn + 64n² )

Removing brackets.

→ 49m² - 112mn + 64n² + 49m² + 112mn + 64n²

Grouping all like terms.

→ 49m² + 49m² - 112mn + 112mn + 64n² + 64n²

Performing addition.

→ 49m² + 49m² + 64n² + 64n²

Performing addition.

$\longrightarrow\underline{\boxed{\large \sf{\: {98m}^{2} + {128n}^{2}}}} \: \red{\bigstar}$

Henceforth, 98m² + 128n² is the answer.

Answer 2

(7m - 8n)² + (7m + 8n)²

= [(7m)² - 2(7m)(8n) + (8n)²] + [(7m)² + 2(7m)(8n) + (8n)²]

∵ (a - b)² = a² - 2ab + b² & (a + b)² = a² + 2ab + b²

= (49m² - 112mn + 64n²) + (49m² + 112mn + 64n²)

= 49m² - 112mn + 64n² + 49m² + 112mn + 64n²

= 98m² + 128n² (answer).