x2-8x-9 by spliting the middle term step by step

To factor the quadratic expression \( x^2 - 8x - 9 \) by splitting the middle term, we can follow these steps:

### Step-by-Step Process:

1. **Identify the quadratic expression**:
   \[
   x^2 - 8x - 9
   \]

2. **Find the product of the first and last term**:
   The first term is \(x^2\) and the last term is \(-9\). Their product is:
   \[
   1 \times (-9) = -9
   \]

3. **Find two numbers that multiply to give the product (-9) and add up to the middle term (-8)**:
   We need two numbers whose product is \(-9\) and sum is \(-8\). These numbers are \(-9\) and \(1\), since:
   \[
   (-9) \times 1 = -9 \quad \text{and} \quad (-9) + 1 = -8
   \]

4. **Rewrite the middle term (-8x) using the two numbers found (-9 and 1)**:
   \[
   x^2 - 9x + 1x - 9
   \]

5. **Group the terms**:
   \[
   (x^2 - 9x) + (1x - 9)
   \]

6. **Factor out the common factor from each group**:
   From \(x^2 - 9x\), factor out \(x\); from \(1x - 9\), factor out \(1\):
   \[
   x(x - 9) + 1(x - 9)
   \]

7. **Factor out the common binomial**:
   The common factor is \((x - 9)\):
   \[
   (x - 9)(x + 1)
   \]

Thus, the factorized form of \(x^2 - 8x - 9\) is:
\[
(x - 9)(x + 1)
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you solve quadratic equations by factoring?
2. Can you apply the same method to factor \(x^2 + 6x + 9\)?
3. What are other ways to solve quadratic equations apart from factoring?
4. How can you check if your factorization is correct?
5. What happens when the quadratic can't be factored easily?

**Tip**: Always check your factorization by expanding the factored form back to its original quadratic expression to ensure accuracy.

x^2 - 8x - 9 by splitting the middle term step by step

Explore how to factor the quadratic expression x^2 - 8x - 9 by splitting the middle term with a step-by-step guide. This solution includes important algebraic concepts, suitable for students in Grades 8-10, and explains the factoring method clearly.

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