Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
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].
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.