Thank you for visiting Factor tex 16z 4 625y 2 tex completely tex 16z 4 625y 2 tex. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To factor the expression [tex]\(16z^4 - 625y^2\)[/tex] completely, follow these steps:
1. Recognize the Structure:
The expression [tex]\(16z^4 - 625y^2\)[/tex] is a difference of squares.
2. Identify Squares:
- [tex]\(16z^4\)[/tex] can be written as [tex]\((4z^2)^2\)[/tex].
- [tex]\(625y^2\)[/tex] can be written as [tex]\((25y)^2\)[/tex].
3. Apply the Difference of Squares Formula:
The difference of squares formula is [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex].
4. Apply to the Expression:
- Here, [tex]\(a = 4z^2\)[/tex] and [tex]\(b = 25y\)[/tex].
- Substitute into the formula:
[tex]\[
16z^4 - 625y^2 = (4z^2 - 25y)(4z^2 + 25y)
\][/tex]
5. Check Further Factorization:
Now, check if each factor, [tex]\(4z^2 - 25y\)[/tex] and [tex]\(4z^2 + 25y\)[/tex], can be factored further.
- [tex]\(4z^2 - 25y\)[/tex] and [tex]\(4z^2 + 25y\)[/tex] are not perfect squares or any special products, so they cannot be factored further over the real numbers.
6. Final Answer:
The completely factored form of [tex]\(16z^4 - 625y^2\)[/tex] is:
[tex]\[
(4z^2 - 25y)(4z^2 + 25y)
\][/tex]
That's the solution to factoring the given expression completely.
1. Recognize the Structure:
The expression [tex]\(16z^4 - 625y^2\)[/tex] is a difference of squares.
2. Identify Squares:
- [tex]\(16z^4\)[/tex] can be written as [tex]\((4z^2)^2\)[/tex].
- [tex]\(625y^2\)[/tex] can be written as [tex]\((25y)^2\)[/tex].
3. Apply the Difference of Squares Formula:
The difference of squares formula is [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex].
4. Apply to the Expression:
- Here, [tex]\(a = 4z^2\)[/tex] and [tex]\(b = 25y\)[/tex].
- Substitute into the formula:
[tex]\[
16z^4 - 625y^2 = (4z^2 - 25y)(4z^2 + 25y)
\][/tex]
5. Check Further Factorization:
Now, check if each factor, [tex]\(4z^2 - 25y\)[/tex] and [tex]\(4z^2 + 25y\)[/tex], can be factored further.
- [tex]\(4z^2 - 25y\)[/tex] and [tex]\(4z^2 + 25y\)[/tex] are not perfect squares or any special products, so they cannot be factored further over the real numbers.
6. Final Answer:
The completely factored form of [tex]\(16z^4 - 625y^2\)[/tex] is:
[tex]\[
(4z^2 - 25y)(4z^2 + 25y)
\][/tex]
That's the solution to factoring the given expression completely.
Thank you for reading the article Factor tex 16z 4 625y 2 tex completely tex 16z 4 625y 2 tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
