We appreciate your visit to Factor completely tex 27x 2 48y 2 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To factor the expression [tex]\(27x^2 - 48y^2\)[/tex] completely, we can follow these steps:
1. Identify a Common Factor: First, observe if there's a greatest common factor (GCF) for the coefficients. Here, both 27 and 48 can be divided by 3. So, we can factor out 3 from the expression:
[tex]\[
27x^2 - 48y^2 = 3(9x^2 - 16y^2)
\][/tex]
2. Recognize a Difference of Squares: The expression [tex]\(9x^2 - 16y^2\)[/tex] is a difference of squares. The difference of squares formula is given by:
[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]
Here, [tex]\(9x^2\)[/tex] is [tex]\((3x)^2\)[/tex] and [tex]\(16y^2\)[/tex] is [tex]\((4y)^2\)[/tex].
3. Apply the Difference of Squares Formula: Using the difference of squares formula, we factor [tex]\(9x^2 - 16y^2\)[/tex] as:
[tex]\[
9x^2 - 16y^2 = (3x - 4y)(3x + 4y)
\][/tex]
4. Write the Final Factorized Expression: Substitute the factored form back into the expression with the common factor we initially took out:
[tex]\[
27x^2 - 48y^2 = 3(3x - 4y)(3x + 4y)
\][/tex]
Therefore, the expression [tex]\(27x^2 - 48y^2\)[/tex] completely factorizes to [tex]\(3(3x - 4y)(3x + 4y)\)[/tex].
1. Identify a Common Factor: First, observe if there's a greatest common factor (GCF) for the coefficients. Here, both 27 and 48 can be divided by 3. So, we can factor out 3 from the expression:
[tex]\[
27x^2 - 48y^2 = 3(9x^2 - 16y^2)
\][/tex]
2. Recognize a Difference of Squares: The expression [tex]\(9x^2 - 16y^2\)[/tex] is a difference of squares. The difference of squares formula is given by:
[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]
Here, [tex]\(9x^2\)[/tex] is [tex]\((3x)^2\)[/tex] and [tex]\(16y^2\)[/tex] is [tex]\((4y)^2\)[/tex].
3. Apply the Difference of Squares Formula: Using the difference of squares formula, we factor [tex]\(9x^2 - 16y^2\)[/tex] as:
[tex]\[
9x^2 - 16y^2 = (3x - 4y)(3x + 4y)
\][/tex]
4. Write the Final Factorized Expression: Substitute the factored form back into the expression with the common factor we initially took out:
[tex]\[
27x^2 - 48y^2 = 3(3x - 4y)(3x + 4y)
\][/tex]
Therefore, the expression [tex]\(27x^2 - 48y^2\)[/tex] completely factorizes to [tex]\(3(3x - 4y)(3x + 4y)\)[/tex].
Thanks for taking the time to read Factor completely tex 27x 2 48y 2 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
