What is the value of `(203 + 107)^(2) - (203 - 107)^(2)` ?

Options

A. 85886
B. 86884
C. 43442
D. 87884

Answer

To solve the expression \((203 + 107)^{2} - (203 - 107)^{2}\), we can use the difference of squares formula, which states that:

\[ a^2 - b^2 = (a - b)(a + b) \]

In our case, we can let:
- \( a = 203 + 107 \)
- \( b = 203 - 107 \)

Now we can calculate \( a \) and \( b \):

1. Calculate \( a \):
\[ a = 203 + 107 = 310 \]

2. Calculate \( b \):
\[ b = 203 - 107 = 96 \]

Now, we can apply the difference of squares formula:

\[ (203 + 107)^{2} - (203 - 107)^{2} = (310)^{2} - (96)^{2} \]

Using the difference of squares formula:

\[ = (310 - 96)(310 + 96) \]

Now, calculate \( 310 - 96 \) and \( 310 + 96 \):

3. Calculate \( 310 - 96 \):
\[ 310 - 96 = 214 \]

4. Calculate \( 310 + 96 \):
\[ 310 + 96 = 406 \]

Now substitute these values back into the expression:

\[ = 214 \times 406 \]

Now, we can calculate \( 214 \times 406 \):

5. Calculate \( 214 \times 406 \):
\[ 214 \times 406 = 86884 \]

Thus, the final value of the expression \((203 + 107)^{2} - (203 - 107)^{2}\) is:

\[ \boxed{86884} \]