Question

Expand the following, using a suitable identity.
                     \[(x+30)(x+30)\]

Answer 1

Hint: In the above type of question we will use the identity and we will get the answer. For the above question we will use the identity \[{{(a+b)}^{2}}=(a+b)(a+b)={{a}^{2}}+2ab+{{b}^{2}}\] by using this identity in the above question we will get the result easily, otherwise we will face some difficulty while simplification without using the identity in these type of problems.

Complete step-by-step answer:
Now we will use the above identity to solve the given question as follow,
\[\begin{align}
  & \Rightarrow (x+30)(x+30)={{(x+30)}^{2}}={{x}^{2}}+2\times 30\times x+{{30}^{2}} \\
 & ={{x}^{2}}+60x+900 \\
\end{align}\]
Here we get the simplification form of the expression given in the question.

Note: Be careful while doing calculation as you can make mistakes and you will get the incorrect answer. Also remember the different identity used in algebra as it makes your approach to the question very quickly in the right direction. Also remember the fact about the identity is that an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variable ) produces the same value for all the values of the variables within a certain range of validity. If an equation satisfies all the values then it will be an identity.