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Solve for [tex]\( x \)[/tex]:
[tex]\[ x^2 - 9 = 0 \][/tex]

Sagot :

GinnyAnswer
Sure, let’s factor the expression [tex]\( x^2 - 9 \)[/tex].

### Step-by-Step Solution

1. Identify the Form:
Notice that the expression [tex]\( x^2 - 9 \)[/tex] is a difference of squares. The difference of squares can be generally written as:
[tex]\[ a^2 - b^2 = (a + b)(a - b) \][/tex]
In this equation, [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are any two terms.

2. Recognize the Terms:
In the given expression [tex]\( x^2 - 9 \)[/tex]:
- [tex]\( a \)[/tex] is [tex]\( x \)[/tex] (since [tex]\( x^2 \)[/tex] is [tex]\( x \)[/tex] squared)
- [tex]\( b \)[/tex] is [tex]\( 3 \)[/tex] (since [tex]\( 9 \)[/tex] is [tex]\( 3 \)[/tex] squared)

3. Apply the Difference of Squares Formula:
Substitute [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the difference of squares formula:
[tex]\[ x^2 - 9 = (x + 3)(x - 3) \][/tex]

### Conclusion
After factoring, the expression [tex]\( x^2 - 9 \)[/tex] can be written as:
[tex]\[ (x + 3)(x - 3) \][/tex]

So, the factorized form of [tex]\( x^2 - 9 \)[/tex] is [tex]\((x + 3)(x - 3)\)[/tex].
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