The value of $$\frac {((56+34)^2-(56-34)^2)}{(4 × 56 × 34)}$$​ is:

Correct option is B

Formula Used:

​$$a^2 - b^2 = (a-b)(a+b)$$​​

Solution:

$$\frac{(56+34)^2 - (56-34)^2}{4 \times 56 \times 34}\\\ \\ = \frac{((56+34) - (56-34))((56+34) + (56-34))}{4 \times 56 \times 34}\\\ \\= \frac{(56 + 34 - (56 - 34))(56 + 34 + (56 - 34))}{4 \times 56 \times 34} \\\ \\= \frac{(34 + 34)(56 + 56)}{4 \times 56 \times 34} \\\ \\ = \frac{68 \times 112}{4 \times 56 \times 34}\\\ \\= \frac{68 \times 112}{7616}\\= 1$$ 

Alternate Method:

$${(a+b)^2-(a-b)^2} = 4ab\\On comparison,a= 56 \, and \, b = 34$$​

$$\frac {((56+34)^2-(56-34)^2)}{(4 × 56 × 34)} = \frac{4 × 56 × 34}{4 × 56 × 34}=1$$​​