Q.

Simplify 4m+5n 2 + 5m+4n 2  .


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a

41 m 2 +41 n 2 +80mn  

b

41 m 2 +41 n 2 80mn  

c

41 m 2 41 n 2 +80mn  

d

41 m 2 +41 n 2 +80mn    

answer is A.

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Detailed Solution

It is given 4m+5n 2 + 5m+4n 2  .
We know the identity a+b 2 = a 2 + b 2 +2ab  .
Expanding the whole square terms by the use of identity,
Let us expand 4m+5n 2   first,
4m+5n 2 = 4m 2 + 5n 2 +2×4m×5n 4m+5n 2 =16 m 2 +25 n 2 +40mn  Now let us expand 5m+4n 2  ,
5m+4n 2 = 5m 2 + 4n 2 +2×5m×4n 5m+4n 2 =25 m 2 +16 n 2 +40mn  
On substituting these values in 4m+5n 2 + 5m+4n 2   we get,
4m+5n 2 + 5m+4n 2 =16 m 2 +25 n 2 +40mn+25 m 2 +16 n 2 +40mn    Adding all m 2  terms together and all n 2   terms together,
4m+5n 2 + 5m+4n 2  = 16+25 m 2 + 25+16 n 2 + 40+40 mn    4m+5n 2 + 5m+4n 2  =41 m 2 +41 n 2 +80mn  
Therefore, 4m+5n 2 + 5m+4n 2  =41 m 2 +41 n 2 +80mn.  
Hence, option (1) is correct.
 
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