Question

If p=0 and q=2, then find the value of equation ${{p}^{2}}+2pq+{{q}^{2}}$.

Answer 1

Hint: First, as we can see it is a very straight forward question as we just want to substitute the values in the equation to get the final answer. Then, we will proceed with the substitution with value p=0 and q=2 in the given equation. Then, we can clearly see that anything raised to power 0 will give 0 and moreover anything multiplied with 0 gives 0 and then we get the final result.

Complete step-by-step answer:
In this question, we are supposed to find the value of the equation as ${{p}^{2}}+2pq+{{q}^{2}}$with p having a value of 0 and q having a value of 2.
So, as we can see it is a very straight forward question as we just want to substitute the values in the equation to get the final answer.
Then, we will proceed with the substitution with value p=0 and q=2 in the given equation as:
${{0}^{2}}+2\left( 0 \right)\left( 2 \right)+{{2}^{2}}$
Now, by solving the above equation, we can get the answer which is required in the question.
As we can see clearly anything raised to power 0 will give 0 and moreover anything multiplied with 0 gives 0.
So, the solution of the equation becomes as:
$\begin{align}
  & {{0}^{2}}+2\left( 0 \right)\left( 2 \right)+{{2}^{2}}=0+0+4 \\
 & \Rightarrow 4 \\
\end{align}$
So, we get the final answer as 4.
Hence the value of the equation ${{p}^{2}}+2pq+{{q}^{2}}$ with p=0 and q=2 is 4.

Note: Now, to solve this question we have another approach as the given expression follows the identity as ${{\left( a+b \right)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}$. Then by using the above identity we need to find the value of ${{p}^{2}}+2pq+{{q}^{2}}={{\left( p+q \right)}^{2}}$. Then by substituting the value of p=0 and q=2, we get:
$\begin{align}
  & {{\left( 0+2 \right)}^{2}}={{2}^{2}} \\
 & \Rightarrow 4 \\
\end{align}$
So, we get the same answer as 4 by this approach also.