Discussion
What is the value of \((469 + 174)^2 - (469 - 174)^2\) / \((469 \times 174)\)?
Answer: B
Use the identity for the difference of two squares of a sum and a difference.
\[ (a+b)^{2} - (a-b)^{2} = 4ab \]
\[ \frac{4ab}{ab} = 4 \]
The actual values 469 and 174 never have to be multiplied out - they cancel entirely.
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