What is the value of
`((941 + 149)^2 + (941 - 149)^2)/((941 xx 941 + 149 xx 149))` ?

Options

A. 10
B. 2
C. 1
D. 100

Answer

To solve the expression

\[ \frac{(941 + 149)^2 + (941 - 149)^2}{941^2 + 149^2} \]

we can use algebraic identities to simplify the calculations.

### Step 1: Define Variables
Let \( A = 941 \) and \( B = 149 \). Then we can rewrite the expression as:

\[ \frac{(A + B)^2 + (A - B)^2}{A^2 + B^2} \]

### Step 2: Expand the Numerator
Using the algebraic identity for the square of a sum and the square of a difference, we have:

\[ (A + B)^2 = A^2 + 2AB + B^2 \]
\[ (A - B)^2 = A^2 - 2AB + B^2 \]

Adding these two expansions together gives:

\[ (A + B)^2 + (A - B)^2 = (A^2 + 2AB + B^2) + (A^2 - 2AB + B^2) = 2A^2 + 2B^2 \]

### Step 3: Substitute Back into the Expression
Now substituting this back into our expression, we get:

\[ \frac{2A^2 + 2B^2}{A^2 + B^2} \]

### Step 4: Factor Out the Common Terms
We can factor out the 2 from the numerator:

\[ = \frac{2(A^2 + B^2)}{A^2 + B^2} \]

### Step 5: Simplify the Expression
Since \( A^2 + B^2 \) is common in the numerator and denominator, we can cancel it out (as long as \( A^2 + B^2 \neq 0 \), which it isn't since both A and B are positive):

\[ = 2 \]

### Final Answer
Thus, the value of the given expression is

\[ \boxed{2} \]