Question

Evaluate using the identities : ${\left(83\right)}^2-{\left(18\right)}^2$

Answer 1

Step 1 : Identify the identity we can use to simplify the question

If we take $a=83andb=18$, the we can clearly see the form of the identity .It is of the form ${\left(a\right)}^2-{\left(b\right)}^2$ which is equal to $(a+b)(a-b)$

Step 2 : Solve the question using the identity

$$\begin{gathered} {\left(83\right)}^2-{\left(18\right)}^2=(83+18)(83-18) \\ =\left(101\right)\left(65\right) \\ =6565 \end{gathered}$$

Hence the result is $6565$