Q : 4        Simplify. 

                (iii)  (7m-8n)^2+(7m+8n)^2

Answers (1)

we use 
(a-b)^{2} = a^{2} -2ab + b^{2}       and     (a+b)^{2} = a^{2} +2ab + b^{2}
 In this a = 7m and b = 8n
                                   (7m-8n)^{2} = (7m)^{2} -2(7m)(8n) + (8n)^{2}
                                                              =49m^{2} -112mn + 64n^{2}
and 
                                   (7m+8n)^{2} = (7m)^{2} +2(7m)(8n) + (8n)^{2}
                                                             =49m^{2} +112mn + 64n^{2}

So,  (7m - 8n)^{2} + (7m + 8n)^{2}   =   49m^{2} -112mn + 64n^{2}  +  49m^{2} +112mn + 64n^{2}
                                                                 =2(49m^{2} + 64n^{2})

or 

remember that

(a-b)^2+(a+b)^2=2(a^2+b^2)

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