Without finding the squares, evaluate the following: 61² - 1

The expression \( 61^2 - 1 \) can be evaluated using the difference of squares formula:

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

Here, \( a = 61 \) and \( b = 1 \). Substituting these into the formula, we get:

\[
61^2 - 1^2 = (61 - 1)(61 + 1) = 60 \times 62
\]

Now, calculate \( 60 \times 62 \):

\[
60 \times 62 = 60 \times (60 + 2) = 60 \times 60 + 60 \times 2 = 3600 + 120 = 3720
\]

So, \( 61^2 - 1 = 3720 \).

Would you like more details on this process or have any questions?

Here are some related questions:
1. How can the difference of squares formula be applied to other problems?
2. What is the general formula for expanding \( (a + b)^2 \)?
3. How does the difference of squares formula help in factorizing expressions?
4. How can you quickly multiply numbers like \( 60 \times 62 \) using mental math?
5. How is the difference of squares related to quadratic equations?

**Tip:** The difference of squares is a powerful tool for simplifying expressions and can save time, especially with larger numbers.

Discover how to evaluate 61 squared minus 1 using the difference of squares formula. Follow a step-by-step explanation, including multiplication techniques for quick calculations. Suitable for Grades 7-9.

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