Answer
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Hint: We will first consider the expression and let ${\text{A}} = (469 + 174)$ and ${\text{B}} = (469 - 174)$. Now, we will use the identity ${{\text{A}}^2} - {{\text{B}}^2} = {\text{(A + B)(A}} - {\text{B)}}$ and substitute the values accordingly. Next, while applying the identity put the values of \[{\text{A}}\] and \[{\text{B}}\] carefully. Further solve the expression and get the value.
Complete step by step solution:
We will first consider the equation given $\dfrac{{{{(469 + 174)}^2} - {{(469 - 174)}^2}}}{{469 \times 174}}$.
Now, we will let ${\text{A}} = (469 + 174)$ and ${\text{B}} = (469 - 174)$.
Next, we will use the formula ${{\text{A}}^2} - {{\text{B}}^2} = {\text{(A + B)(A}} - {\text{B)}}$
Let us take the given expression $\dfrac{{{{(469 + 174)}^2} - {{(469 - 174)}^2}}}{{469 \times 174}}$ as equation $\left( 1 \right)$
Now, put the values in equation (1) as ${\text{A}} = (469 + 174)$ and ${\text{B}} = (469 - 174)$.
Use formula of ${{\text{A}}^2} - {{\text{B}}^2}$in equation $\left( 1 \right)$
Thus, we get,
$
\Rightarrow \dfrac{{\left( {\left( {469 + 174} \right) + \left( {469 - 174} \right)} \right)\left( {\left( {469 + 174} \right) - \left( {469 - 174} \right)} \right)}}{{469 \times 174}} \\
\Rightarrow \dfrac{{(2 \times 469)(2 \times 174)}}{{469 \times 174}} \\
\Rightarrow 2 \times 2 \\
\Rightarrow 4 \\
$
Hence, we get the value of the given expression as 4.
Thus, option B is the correct answer.
Note: Don’t simplify the question initially because it can lead the question in a very complex calculation. Use the identity ${{\text{A}}^2} - {{\text{B}}^2} = {\text{(A + B)(A}} - {\text{B)}}$ to simplify the expression and get the value. While substituting the values of \[{\text{A}}\] and \[{\text{B}}\] in the identity use the brackets for separation of numbers. Do not multiply the numerator else cut with the values in the denominator to simplify the calculations.
Complete step by step solution:
We will first consider the equation given $\dfrac{{{{(469 + 174)}^2} - {{(469 - 174)}^2}}}{{469 \times 174}}$.
Now, we will let ${\text{A}} = (469 + 174)$ and ${\text{B}} = (469 - 174)$.
Next, we will use the formula ${{\text{A}}^2} - {{\text{B}}^2} = {\text{(A + B)(A}} - {\text{B)}}$
Let us take the given expression $\dfrac{{{{(469 + 174)}^2} - {{(469 - 174)}^2}}}{{469 \times 174}}$ as equation $\left( 1 \right)$
Now, put the values in equation (1) as ${\text{A}} = (469 + 174)$ and ${\text{B}} = (469 - 174)$.
Use formula of ${{\text{A}}^2} - {{\text{B}}^2}$in equation $\left( 1 \right)$
Thus, we get,
$
\Rightarrow \dfrac{{\left( {\left( {469 + 174} \right) + \left( {469 - 174} \right)} \right)\left( {\left( {469 + 174} \right) - \left( {469 - 174} \right)} \right)}}{{469 \times 174}} \\
\Rightarrow \dfrac{{(2 \times 469)(2 \times 174)}}{{469 \times 174}} \\
\Rightarrow 2 \times 2 \\
\Rightarrow 4 \\
$
Hence, we get the value of the given expression as 4.
Thus, option B is the correct answer.
Note: Don’t simplify the question initially because it can lead the question in a very complex calculation. Use the identity ${{\text{A}}^2} - {{\text{B}}^2} = {\text{(A + B)(A}} - {\text{B)}}$ to simplify the expression and get the value. While substituting the values of \[{\text{A}}\] and \[{\text{B}}\] in the identity use the brackets for separation of numbers. Do not multiply the numerator else cut with the values in the denominator to simplify the calculations.
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