What Is The Completely Factored Form Of $25x^4 - 16y^2$?A. $(5x^4 + 4y)(5x - 4y)$ B. \$(5x^3 + 4y)(5x^2 - 4y)$[/tex\] C. $(5x^2 + 4y)(5x^2 - 4y)$ D. $25x^4 - 16y^2$
What is the Completely Factored Form of $25x^4 - 16y^2$?
In mathematics, factoring is a fundamental concept that involves expressing an algebraic expression as a product of simpler expressions. Factoring is an essential skill in algebra, and it has numerous applications in various fields, including mathematics, science, and engineering. In this article, we will explore the completely factored form of the expression $25x^4 - 16y^2$.
The given expression is $25x^4 - 16y^2$. This expression consists of two terms: $25x^4$ and $-16y^2$. The first term is a polynomial of degree 4, while the second term is a polynomial of degree 2. To factor this expression, we need to find a way to express it as a product of simpler expressions.
To factor the expression $25x^4 - 16y^2$, we can use the difference of squares formula. The difference of squares formula states that:
We can rewrite the expression $25x^4 - 16y^2$ as:
Now, we can apply the difference of squares formula:
Therefore, the completely factored form of the expression $25x^4 - 16y^2$ is:
Now, let's compare our result with the options provided:
A. $(5x^4 + 4y)(5x - 4y)$
B. $(5x^3 + 4y)(5x^2 - 4y)$
C. $(5x^2 + 4y)(5x^2 - 4y)$
D. $25x^4 - 16y^2$
Our result matches option C. Therefore, the completely factored form of the expression $25x^4 - 16y^2$ is:
In this article, we explored the completely factored form of the expression $25x^4 - 16y^2$. We used the difference of squares formula to factor the expression and obtained the result:
This result matches option C, which is the correct answer. Factoring is an essential skill in algebra, and it has numerous applications in various fields. We hope that this article has provided a clear understanding of the completely factored form of the expression $25x^4 - 16y^2$.
The completely factored form of the expression $25x^4 - 16y^2$ is:
(5x^2 + 4y)(5x^2 - 4y)$<br/> **Q&A: Factoring the Expression $25x^4 - 16y^2$** ===================================================== **Introduction** =============== In our previous article, we explored the completely factored form of the expression $25x^4 - 16y^2$. We used the difference of squares formula to factor the expression and obtained the result: $(5x^2 + 4y)(5x^2 - 4y)
In this article, we will answer some frequently asked questions about factoring the expression $25x^4 - 16y^2$.
Q: What is the difference of squares formula?
A: The difference of squares formula is a mathematical formula that states:
This formula can be used to factor expressions of the form $a^2 - b^2$.
Q: How do I apply the difference of squares formula to the expression $25x^4 - 16y^2$?
A: To apply the difference of squares formula to the expression $25x^4 - 16y^2$, we need to rewrite it in the form $a^2 - b^2$. We can do this by factoring out the greatest common factor of the two terms:
Now, we can apply the difference of squares formula:
Q: What is the completely factored form of the expression $25x^4 - 16y^2$?
A: The completely factored form of the expression $25x^4 - 16y^2$ is:
Q: How do I know if an expression can be factored using the difference of squares formula?
A: To determine if an expression can be factored using the difference of squares formula, we need to check if it is in the form $a^2 - b^2$. If it is, then we can apply the formula to factor the expression.
Q: What are some common mistakes to avoid when factoring expressions using the difference of squares formula?
A: Some common mistakes to avoid when factoring expressions using the difference of squares formula include:
- Not rewriting the expression in the form $a^2 - b^2$ before applying the formula
- Not factoring out the greatest common factor of the two terms
- Not applying the formula correctly
Q: How do I check if my factored expression is correct?
A: To check if your factored expression is correct, you can multiply the two factors together and see if you get the original expression. If you do, then your factored expression is correct.
In this article, we answered some frequently asked questions about factoring the expression $25x^4 - 16y^2$. We hope that this article has provided a clear understanding of the difference of squares formula and how to apply it to factor expressions. If you have any further questions, please don't hesitate to ask.
The completely factored form of the expression $25x^4 - 16y^2$ is: