Question

Find the value of ${{984}^{2}}-{{16}^{2}}$

Answer 1

Hint: We solve this question by first considering the formula for the algebraic expression, ${{a}^{2}}-{{b}^{2}}=\left( a-b \right)\left( a+b \right)$. Then we compare our expression with this formula and use the formula with the values accordingly. Then we find the values of both terms in the product. Then we multiply them to find the required result.

Complete step-by-step solution
We are asked to find the value of ${{984}^{2}}-{{16}^{2}}$.
To solve this expression let us consider the formula,
${{a}^{2}}-{{b}^{2}}=\left( a-b \right)\left( a+b \right)$
Here comparing the above formula with our given expression, ${{984}^{2}}-{{16}^{2}}$ we can say that,
$\Rightarrow a=984$
Similarly, we can write the other as,
$\Rightarrow b=16$
So, by using the above formula we can write the value of ${{984}^{2}}-{{16}^{2}}$ as,
$\Rightarrow \left( 984+16 \right)\left( 984-16 \right).............\left( 1 \right)$
Now let us consider the first term in the above product, that is $\left( 984+16 \right)$. We can find its value as,
$\Rightarrow 984+16=1000............\left( 2 \right)$
Now let us consider the second term in the above product, that is $\left( 984-16 \right)$. We can find its value as,
$\Rightarrow 984-16=968..............\left( 3 \right)$
Now let us substitute the values in equation (2) and equation (3) in equation (1). Then we get,
$\begin{align}
  & \Rightarrow \left( 984+16 \right)\left( 984-16 \right) \\
 & \Rightarrow \left( 1000 \right)\left( 968 \right) \\
 & \Rightarrow 968000 \\
\end{align}$
So, we get the value of ${{984}^{2}}-{{16}^{2}}$ as 968000.
Hence the answer is 968000.

Note: The common mistake one makes while solving this problem is one might take the formula for the algebraic expression, ${{a}^{2}}-{{b}^{2}}$ wrongly as, ${{a}^{2}}-{{b}^{2}}={{\left( a-b \right)}^{2}}$. But it is wrong as the formula for ${{\left( a-b \right)}^{2}}$ is ${{\left( a-b \right)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}$.
We can also solve this question in another process by finding the value of ${{984}^{2}}$ and ${{16}^{2}}$. Then by subtracting them but it takes a long process as calculating the value of ${{984}^{2}}$ takes more time. So, it is better to use the formula and solve it as we did in the solution part.