Simplify. Express your answer as a single term using exponents.

(1 point)
1785 ×1789 = ?

1 answer

To simplify the expression \( 1785 \times 1789 \) in terms of exponents, we can use the identity for the product of two numbers that are evenly spaced around a midpoint.

We can rewrite the numbers as follows:

\[ 1785 = 1787 - 2 \] \[ 1789 = 1787 + 2 \]

Thus, we can express the product as:

\[ (1787 - 2)(1787 + 2) \]

This is a difference of squares, which can be simplified using the formula \( (a - b)(a + b) = a^2 - b^2 \).

Letting \( a = 1787 \) and \( b = 2 \), we have:

\[ (1787 - 2)(1787 + 2) = 1787^2 - 2^2 \]

Now we calculate \( 2^2 \):

\[ 2^2 = 4 \]

Therefore, the expression simplifies to:

\[ 1787^2 - 4 \]

This can't be simplified further without calculating \( 1787^2 \). The final answer expressed as a single term using exponents is:

\[ 1787^2 - 4 \]