Evaluate the following using suitable identities: 
1) 102² 
2) 49² 
3) 75 x 65 
4) 102 x 103 

Dear Student,

$$\begin{gathered} 1) We have, \\ {102}^2 \\ We can write it as, \\ {\left(100+2\right)}^2 \\ U\sin g identity: {\left(a+b\right)}^2=a^2+b^2+2ab \\ here, a=100 and b=2 \\ {\left(100+2\right)}^2={100}^2+2^2+2\times 100\times 2=10000+4+400=10404 \\ 3) We have, \\ 75\times 65 \\ We can write it as, \\ \left(70+5\right)\left(70-5\right) \\ U\sin g identity, \\ \left(a+b\right)\left(a-b\right)=a^2-b^2 \\ here, a=70 and b=5 \\ now, \\ \left(70+5\right)\left(70-5\right)={70}^2-5^2=4900-25=4875 \end{gathered}$$

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