Thank you for visiting Factor the expression tex 16x 4 625 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 :
We start with the expression:
[tex]$$ 16x^4 - 625. $$[/tex]
Step 1: Recognize a Difference of Squares
Notice that both terms are perfect squares:
- [tex]$16x^4 = (4x^2)^2$[/tex]
- [tex]$625 = 25^2$[/tex]
Thus, the expression can be written as a difference of two squares:
[tex]$$ 16x^4 - 625 = (4x^2)^2 - 25^2. $$[/tex]
Using the formula for the difference of squares,
[tex]$$ a^2 - b^2 = (a - b)(a + b), $$[/tex]
with [tex]$a = 4x^2$[/tex] and [tex]$b = 25$[/tex], we have:
[tex]$$ (4x^2)^2 - 25^2 = (4x^2 - 25)(4x^2 + 25). $$[/tex]
Step 2: Factor the Difference of Squares Again
Now, focus on the first factor:
[tex]$$ 4x^2 - 25. $$[/tex]
This too is a difference of two squares since:
- [tex]$4x^2 = (2x)^2$[/tex]
- [tex]$25 = 5^2$[/tex]
Using the difference of squares formula once more:
[tex]$$ 4x^2 - 25 = (2x - 5)(2x + 5). $$[/tex]
Step 3: Write the Fully Factored Form
The second factor, [tex]$4x^2 + 25$[/tex], is a sum of squares, which does not factor further over the real numbers.
Thus, the completely factored form of the original expression is:
[tex]$$ 16x^4 - 625 = (2x - 5)(2x + 5)(4x^2 + 25). $$[/tex]
This is the final result.
[tex]$$ 16x^4 - 625. $$[/tex]
Step 1: Recognize a Difference of Squares
Notice that both terms are perfect squares:
- [tex]$16x^4 = (4x^2)^2$[/tex]
- [tex]$625 = 25^2$[/tex]
Thus, the expression can be written as a difference of two squares:
[tex]$$ 16x^4 - 625 = (4x^2)^2 - 25^2. $$[/tex]
Using the formula for the difference of squares,
[tex]$$ a^2 - b^2 = (a - b)(a + b), $$[/tex]
with [tex]$a = 4x^2$[/tex] and [tex]$b = 25$[/tex], we have:
[tex]$$ (4x^2)^2 - 25^2 = (4x^2 - 25)(4x^2 + 25). $$[/tex]
Step 2: Factor the Difference of Squares Again
Now, focus on the first factor:
[tex]$$ 4x^2 - 25. $$[/tex]
This too is a difference of two squares since:
- [tex]$4x^2 = (2x)^2$[/tex]
- [tex]$25 = 5^2$[/tex]
Using the difference of squares formula once more:
[tex]$$ 4x^2 - 25 = (2x - 5)(2x + 5). $$[/tex]
Step 3: Write the Fully Factored Form
The second factor, [tex]$4x^2 + 25$[/tex], is a sum of squares, which does not factor further over the real numbers.
Thus, the completely factored form of the original expression is:
[tex]$$ 16x^4 - 625 = (2x - 5)(2x + 5)(4x^2 + 25). $$[/tex]
This is the final result.
Thank you for reading the article Factor the expression tex 16x 4 625 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
