Thank you for visiting Factor completely tex x 4 625y 4 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]\(x^4 - 625y^4\)[/tex] completely, we can use the difference of squares method. Here's a step-by-step guide to solving it:
1. Recognize the structure of the expression:
The expression [tex]\(x^4 - 625y^4\)[/tex] is a difference of squares. It can be rewritten as:
[tex]\[
x^4 - (25y^2)^2
\][/tex]
Here, [tex]\(x^4\)[/tex] is [tex]\( (x^2)^2 \)[/tex] and [tex]\(625y^4\)[/tex] is [tex]\((25y^2)^2\)[/tex].
2. Apply the difference of squares formula:
The difference of squares formula is:
[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]
Applying this formula, we get:
[tex]\[
x^4 - (25y^2)^2 = (x^2 - 25y^2)(x^2 + 25y^2)
\][/tex]
3. Further factor the first term, [tex]\(x^2 - 25y^2\)[/tex]:
Notice that [tex]\(x^2 - 25y^2\)[/tex] is also a difference of squares:
[tex]\[
x^2 - (5y)^2
\][/tex]
Again, using the difference of squares formula, we have:
[tex]\[
x^2 - 25y^2 = (x - 5y)(x + 5y)
\][/tex]
4. Combine all parts to get the fully factored form:
Substitute the factored form of [tex]\(x^2 - 25y^2\)[/tex] back into the expression:
[tex]\[
x^4 - 625y^4 = (x - 5y)(x + 5y)(x^2 + 25y^2)
\][/tex]
So, the completely factored form of the expression [tex]\(x^4 - 625y^4\)[/tex] is:
[tex]\[
(x - 5y)(x + 5y)(x^2 + 25y^2)
\][/tex]
1. Recognize the structure of the expression:
The expression [tex]\(x^4 - 625y^4\)[/tex] is a difference of squares. It can be rewritten as:
[tex]\[
x^4 - (25y^2)^2
\][/tex]
Here, [tex]\(x^4\)[/tex] is [tex]\( (x^2)^2 \)[/tex] and [tex]\(625y^4\)[/tex] is [tex]\((25y^2)^2\)[/tex].
2. Apply the difference of squares formula:
The difference of squares formula is:
[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]
Applying this formula, we get:
[tex]\[
x^4 - (25y^2)^2 = (x^2 - 25y^2)(x^2 + 25y^2)
\][/tex]
3. Further factor the first term, [tex]\(x^2 - 25y^2\)[/tex]:
Notice that [tex]\(x^2 - 25y^2\)[/tex] is also a difference of squares:
[tex]\[
x^2 - (5y)^2
\][/tex]
Again, using the difference of squares formula, we have:
[tex]\[
x^2 - 25y^2 = (x - 5y)(x + 5y)
\][/tex]
4. Combine all parts to get the fully factored form:
Substitute the factored form of [tex]\(x^2 - 25y^2\)[/tex] back into the expression:
[tex]\[
x^4 - 625y^4 = (x - 5y)(x + 5y)(x^2 + 25y^2)
\][/tex]
So, the completely factored form of the expression [tex]\(x^4 - 625y^4\)[/tex] is:
[tex]\[
(x - 5y)(x + 5y)(x^2 + 25y^2)
\][/tex]
Thank you for reading the article Factor completely tex x 4 625y 4 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
