To expand \((x - 9)^2\) without directly using the formula, we can simply multiply \((x - 9)\) by itself.

Let's proceed step-by-step:

\[
(x - 9)^2 = (x - 9)(x - 9)
\]

Now, we distribute each term in the first binomial to each term in the second binomial:

1. Multiply \(x\) by \(x\): 
   \[
   x \times x = x^2
   \]

2. Multiply \(x\) by \(-9\): 
   \[
   x \times -9 = -9x
   \]

3. Multiply \(-9\) by \(x\): 
   \[
   -9 \times x = -9x
   \]

4. Multiply \(-9\) by \(-9\): 
   \[
   -9 \times -9 = 81
   \]

Now, combine all the terms:
\[
x^2 - 9x - 9x + 81
\]

Simplify the like terms:
\[
x^2 - 18x + 81
\]

So, the expansion of \((x - 9)^2\) is:
\[
x^2 - 18x + 81
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How would you expand \((x + a)^2\)?
2. What happens when you expand \((x - 9)(x + 9)\)?
3. Can you expand \((2x - 3)^2\)?
4. How can you factor \(x^2 - 18x + 81\) back into binomials?
5. What is the expanded form of \((x - 9)^3\)?

**Tip**: When expanding binomials manually, always distribute each term carefully to avoid mistakes.

Learn how to expand (x-9)^2 step-by-step without using the binomial formula. This example focuses on the distributive property and the FOIL method, providing a clear explanation for students in Grades 8-10.

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