Without finding the squares, evaluate the following: 79² - 1

To evaluate \( 79^2 - 1 \) without finding the square of 79 directly, we can use the difference of squares formula:

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

Here, \( a = 79 \) and \( b = 1 \). Substituting into the formula:

\[
79^2 - 1^2 = (79 - 1)(79 + 1) = 78 \times 80
\]

Now, calculate \( 78 \times 80 \):

\[
78 \times 80 = 78 \times (8 \times 10) = (78 \times 8) \times 10
\]

First, calculate \( 78 \times 8 \):

\[
78 \times 8 = (80 - 2) \times 8 = (80 \times 8) - (2 \times 8) = 640 - 16 = 624
\]

Then, multiply by 10:

\[
624 \times 10 = 6240
\]

So, \( 79^2 - 1 = 6240 \).

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

Here are some related questions:
1. How can you use the difference of squares formula in factorization problems?
2. What is the advantage of using the difference of squares method for calculations?
3. Can you apply the difference of squares formula to other numbers like \( 99^2 - 1 \)?
4. How does mental math help in solving problems like \( 78 \times 80 \)?
5. How can you generalize this method for any number \( n^2 - 1 \)?

**Tip:** Breaking down multiplications into simpler steps, like using mental math tricks, can make calculations faster and easier.

Learn how to evaluate 79 squared minus 1 without direct calculation using the difference of squares formula. This problem involves applying algebraic concepts like the difference of squares, multiplication strategies, and mental math. Suitable for students in Grades 6-8.

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