Question

(8n - 7m)² - (7m – 8n ) ²​

Answer 1

$8n {}^{2} - 7m {}^{2} - 8n {}^{2} - 7m {}^{2}$

$8n {}^{2} - 8n {}^{2} - 7m {}^{2} - 7m {}^{2}$

$0 - 0 \\ = 0$

Answer 2

To find : value of  $(8n -7m)^{2} - (7m -8n )^{2}$

Solution :  

• To find the value of given expression we apply identity given below ,
• $a^{2} - b^{2} = (a + b ) (a -b )$
• In the given expression , $a = 8n-7m$ and $b =7m-8n$ .

• Applying identity to find the value  ,

       $(8n -7m)^{2} - (7m -8n )^{2}$  

       $= [(8n-7m) +(7m -8n )][(8n-7m)- (7m -8n )] \\=[8n-7m+ 7m -8n][8n-7m-7m+ 8n] \\= [0][16n-14n ]\\=0$

Hence , the value of $(8n -7m)^{2} - (7m -8n )^{2}$  is $0$ .