Q : 4     Simplify. 

             (iv) (4m+5n)^2+(5m+4n)^2

Answers (1)

we use 
        (a+b)^{2} = a^{2} +2ab + b^{2}
 1 )   In this a = 4m and b = 5n
                    
                     (4m+5n)^{2} = (4m)^{2} +2(4m)(5n) + (5n)^{2}
                                                = 16m^{2} +40mn + 25n^{2}
2 )      in this  a = 5m and b = 4n 
                                          (5m+4n)^{2} = (5m)^{2} +2(5m)(4n) + (4n)^{2}
                                                                    =    25m^{2} +40mn + 16n^{2}
 
So,      (4m + 5n)^{2} + (5m + 4n)^{2}  =   16m^{2} +40mn + 25n^{2}  +  25m^{2} +40mn + 16n^{2}
                                                                     =   41m^{2} +80mn + 41n^{2}

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