Answer :
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].
### 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].
