Question

Choose an equivalent expression for 123 • 129 • 124 • 122.
124
1218
1235
12216

Answer 1

To simplify the expression \( 123 \cdot 129 \cdot 124 \cdot 122 \), we can utilize some algebraic identities or simplifications.

Notice that we can group the numbers as follows:

\[
123 \cdot 129 \cdot 124 \cdot 122 = (123 \cdot 129) \cdot (124 \cdot 122)
\]

We can calculate \( 123 \cdot 129 \) and \( 124 \cdot 122 \):

1. Calculate \( 123 \cdot 129 \):
\[
123 \cdot 129 = (126 - 3)(126 + 3) = 126^2 - 3^2 = 15876 - 9 = 15867
\]

2. Calculate \( 124 \cdot 122 \):
\[
124 \cdot 122 = (123 + 1)(123 - 1) = 123^2 - 1^2 = 15129 - 1 = 15128
\]

Now combine both products:
\[
123 \cdot 129 \cdot 124 \cdot 122 = 15867 \cdot 15128
\]

This product is quite large and does not directly yield a simpler expression without calculating the full value. However, without the need to calculate the entire product, we note that the options given are significantly smaller.

Given the nature of this problem, it seems to suggest that we choose a value from the options provided, rather than calculating out the full product.

None of the values \(124\), \(1218\), \(1235\), or \(12216\) are explicitly equal to the entire product directly, but considering the numerical size, it appears that \(12216\) could represent the approximate magnitude related to the factors involved.

Thus, after evaluating the numerical values, an acceptable answer from the provided options could be:

\[
\boxed{12216}
\]

This is a choice based on comparative size to the large product of the multiplication rather than an explicit equality.