Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To determine which of the given algebraic expressions represent a difference of squares, we need to recall that a difference of squares takes the form [tex]\( A^2 - B^2 \)[/tex], where both [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are perfect squares.
Let's analyze each expression individually:
### 1. Expression: [tex]\( 9m^4 - 49n^6 \)[/tex]
- Identify components: [tex]\( 9m^4 \)[/tex] and [tex]\( 49n^6 \)[/tex]
- Check if each term is a perfect square:
- [tex]\( 9m^4 \)[/tex] can be rewritten as [tex]\( (3m^2)^2 \)[/tex]
- [tex]\( 49n^6 \)[/tex] can be rewritten as [tex]\( (7n^3)^2 \)[/tex]
Both terms are perfect squares (since [tex]\( 9m^4 = (3m^2)^2 \)[/tex] and [tex]\( 49n^6 = (7n^3)^2 \)[/tex]), so this expression is a difference of squares.
### 2. Expression: [tex]\( 32a^2 - 81n^2 \)[/tex]
- Identify components: [tex]\( 32a^2 \)[/tex] and [tex]\( 81n^2 \)[/tex]
- Check if each term is a perfect square:
- [tex]\( 32a^2 \)[/tex] is not a perfect square because 32 is not a perfect square (since [tex]\(\sqrt{32}\)[/tex] is not an integer)
- [tex]\( 81n^2 \)[/tex] can be rewritten as [tex]\( (9n)^2 \)[/tex], which is a perfect square
Since [tex]\( 32a^2 \)[/tex] is not a perfect square, this expression is not a difference of squares.
### 3. Expression: [tex]\( 16h^2 - 21t^{10} \)[/tex]
- Identify components: [tex]\( 16h^2 \)[/tex] and [tex]\( 21t^{10} \)[/tex]
- Check if each term is a perfect square:
- [tex]\( 16h^2 \)[/tex] can be rewritten as [tex]\( (4h)^2 \)[/tex]
- [tex]\( 21t^{10} \)[/tex] is not a perfect square because 21 is not a perfect square (since [tex]\(\sqrt{21}\)[/tex] is not an integer)
Since [tex]\( 21t^{10} \)[/tex] is not a perfect square, this expression is not a difference of squares.
### 4. Expression: [tex]\( 100x^2 - 10y^4 \)[/tex]
- Identify components: [tex]\( 100x^2 \)[/tex] and [tex]\( 10y^4 \)[/tex]
- Check if each term is a perfect square:
- [tex]\( 100x^2 \)[/tex] can be rewritten as [tex]\( (10x)^2 \)[/tex]
- [tex]\( 10y^4 \)[/tex] is not a perfect square because 10 is not a perfect square (since [tex]\(\sqrt{10}\)[/tex] is not an integer)
Since [tex]\( 10y^4 \)[/tex] is not a perfect square, this expression is not a difference of squares.
### Conclusion:
After analyzing each expression, we find that only the first expression [tex]\( 9m^4 - 49n^6 \)[/tex] is a difference of squares.
Hence, the expression that is a difference of squares is:
[tex]\[ 9m^4 - 49n^6 \][/tex]
Let's analyze each expression individually:
### 1. Expression: [tex]\( 9m^4 - 49n^6 \)[/tex]
- Identify components: [tex]\( 9m^4 \)[/tex] and [tex]\( 49n^6 \)[/tex]
- Check if each term is a perfect square:
- [tex]\( 9m^4 \)[/tex] can be rewritten as [tex]\( (3m^2)^2 \)[/tex]
- [tex]\( 49n^6 \)[/tex] can be rewritten as [tex]\( (7n^3)^2 \)[/tex]
Both terms are perfect squares (since [tex]\( 9m^4 = (3m^2)^2 \)[/tex] and [tex]\( 49n^6 = (7n^3)^2 \)[/tex]), so this expression is a difference of squares.
### 2. Expression: [tex]\( 32a^2 - 81n^2 \)[/tex]
- Identify components: [tex]\( 32a^2 \)[/tex] and [tex]\( 81n^2 \)[/tex]
- Check if each term is a perfect square:
- [tex]\( 32a^2 \)[/tex] is not a perfect square because 32 is not a perfect square (since [tex]\(\sqrt{32}\)[/tex] is not an integer)
- [tex]\( 81n^2 \)[/tex] can be rewritten as [tex]\( (9n)^2 \)[/tex], which is a perfect square
Since [tex]\( 32a^2 \)[/tex] is not a perfect square, this expression is not a difference of squares.
### 3. Expression: [tex]\( 16h^2 - 21t^{10} \)[/tex]
- Identify components: [tex]\( 16h^2 \)[/tex] and [tex]\( 21t^{10} \)[/tex]
- Check if each term is a perfect square:
- [tex]\( 16h^2 \)[/tex] can be rewritten as [tex]\( (4h)^2 \)[/tex]
- [tex]\( 21t^{10} \)[/tex] is not a perfect square because 21 is not a perfect square (since [tex]\(\sqrt{21}\)[/tex] is not an integer)
Since [tex]\( 21t^{10} \)[/tex] is not a perfect square, this expression is not a difference of squares.
### 4. Expression: [tex]\( 100x^2 - 10y^4 \)[/tex]
- Identify components: [tex]\( 100x^2 \)[/tex] and [tex]\( 10y^4 \)[/tex]
- Check if each term is a perfect square:
- [tex]\( 100x^2 \)[/tex] can be rewritten as [tex]\( (10x)^2 \)[/tex]
- [tex]\( 10y^4 \)[/tex] is not a perfect square because 10 is not a perfect square (since [tex]\(\sqrt{10}\)[/tex] is not an integer)
Since [tex]\( 10y^4 \)[/tex] is not a perfect square, this expression is not a difference of squares.
### Conclusion:
After analyzing each expression, we find that only the first expression [tex]\( 9m^4 - 49n^6 \)[/tex] is a difference of squares.
Hence, the expression that is a difference of squares is:
[tex]\[ 9m^4 - 49n^6 \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
