# What will come in place of '?' $\frac{(469\ +\ 174)^2\ -\ (469\ -\ 174)^2}{469\ \times\ 174}=?$

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What will come in place of '?'

$\frac{(469\ +\ 174)^2\ -\ (469\ -\ 174)^2}{469\ \times\ 174}=?$

1. 295
2. 4
3. 2
4. 643

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Correct Answer - Option 2 : 4

Given:

$\frac{(469\ +\ 174)^2\ -\ (469\ -\ 174)^2}{469\ \times\ 174}=?$

Concept Used:

a2 - b2 = (a + b)(a - b)

Calculation:

$\frac{(469\ +\ 174)^2\ -\ (469\ -\ 174)^2}{469\ \times\ 174}=?$

⇒ $\frac{(469 +174 + 469 -174)[(469 + 174) - (469 - 174)]}{469 × 174}$

⇒ $\frac{(2 × 469)(469 +174 -469 +174)}{469 × 174}$

⇒ $\frac{(2 × 469 × 2 × 174)}{469 × 174}$

⇒ 2 × 2

⇒ 4

∴ The value that will come in place of '?' is 4.