What would be the result of the following expression
`(832 xx 832 xx 832 +168 xx 168 xx168)/(832 xx 832-832 xx 168 +168 xx168)`

Options

A. 664
B. 1000
C. 1
D. 4

Answer

To solve the expression \((832 \times 832 \times 832 + 168 \times 168 \times 168) / (832 \times 832 - 832 \times 168 + 168 \times 168)\), we can use the identity for the sum of cubes and the difference of squares.

### Step 1: Rewrite the expression using cubes
The expression can be rewritten as:
\[ \frac{832^3 + 168^3}{832^2 - 832 \times 168 + 168^2} \]

### Step 2: Apply the sum of cubes identity
We can use the identity for the sum of cubes:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]
Here, let \(a = 832\) and \(b = 168\). Thus, we have:
\[ 832^3 + 168^3 = (832 + 168)(832^2 - 832 \times 168 + 168^2) \]

### Step 3: Substitute into the expression
Substituting this back into our expression gives:
\[ \frac{(832 + 168)(832^2 - 832 \times 168 + 168^2)}{832^2 - 832 \times 168 + 168^2} \]

### Step 4: Simplify the expression
The \((832^2 - 832 \times 168 + 168^2)\) terms in the numerator and denominator cancel out:
\[ 832 + 168 \]

### Step 5: Calculate the sum
Now, we can calculate:
\[ 832 + 168 = 1000 \]

### Final Result
Thus, the result of the expression is:
\[ \boxed{1000} \]