To simplify \( 1785 \times 1789 \), we can express each number in a more manageable form.
Notice that: \[ 1785 = 1787 - 2 \quad \text{and} \quad 1789 = 1787 + 2 \]
So, we can rewrite the multiplication as: \[ 1785 \times 1789 = (1787 - 2)(1787 + 2) \]
This expression can be recognized as a difference of squares: \[ (a - b)(a + b) = a^2 - b^2 \] where \( a = 1787 \) and \( b = 2 \).
Applying the difference of squares formula, we have: \[ (1787 - 2)(1787 + 2) = 1787^2 - 2^2 \]
Calculating \( 2^2 \): \[ 2^2 = 4 \]
Now, we express the original multiplication as: \[ 1785 \times 1789 = 1787^2 - 4 \]
Thus, the simplified expression is: \[ 1787^2 - 4 \]
If you wish to keep the answer in exponents: \[ 1785 \times 1789 = 1787^2 - 4 \]
This is the simplest form we can provide as a single term using exponents.
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