We appreciate your visit to Factor the expression 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 :
Let's solve the expression [tex]\(27x^2 - 48y^2\)[/tex] by simplifying or factoring it, if possible.
This expression can be recognized as a difference of squares. The difference of squares formula is given by:
[tex]\[ a^2 - b^2 = (a + b)(a - b) \][/tex]
However, before applying the difference of squares formula, let's see if we can factor out any common factors from the expression first.
1. Identify the Greatest Common Factor (GCF):
The GCF of [tex]\(27x^2\)[/tex] and [tex]\(48y^2\)[/tex] is 3. Let's factor out 3 from the expression:
[tex]\[ 27x^2 - 48y^2 = 3(9x^2 - 16y^2) \][/tex]
2. Factor the Expression Inside the Parentheses:
Now, within the parentheses, [tex]\(9x^2 - 16y^2\)[/tex] is a difference of squares because:
- [tex]\(9x^2\)[/tex] is [tex]\((3x)^2\)[/tex]
- [tex]\(16y^2\)[/tex] is [tex]\((4y)^2\)[/tex]
We can apply the difference of squares formula:
[tex]\[ 9x^2 - 16y^2 = (3x + 4y)(3x - 4y) \][/tex]
3. Combine Everything:
Now plug it back into the expression we factored the GCF out of:
[tex]\[ 27x^2 - 48y^2 = 3(3x + 4y)(3x - 4y) \][/tex]
So, the fully factored form of the expression [tex]\(27x^2 - 48y^2\)[/tex] is:
[tex]\[ 3(3x + 4y)(3x - 4y) \][/tex]
This solution involves recognizing the structure of the expression, identifying the difference of squares, and applying the appropriate factoring steps.
This expression can be recognized as a difference of squares. The difference of squares formula is given by:
[tex]\[ a^2 - b^2 = (a + b)(a - b) \][/tex]
However, before applying the difference of squares formula, let's see if we can factor out any common factors from the expression first.
1. Identify the Greatest Common Factor (GCF):
The GCF of [tex]\(27x^2\)[/tex] and [tex]\(48y^2\)[/tex] is 3. Let's factor out 3 from the expression:
[tex]\[ 27x^2 - 48y^2 = 3(9x^2 - 16y^2) \][/tex]
2. Factor the Expression Inside the Parentheses:
Now, within the parentheses, [tex]\(9x^2 - 16y^2\)[/tex] is a difference of squares because:
- [tex]\(9x^2\)[/tex] is [tex]\((3x)^2\)[/tex]
- [tex]\(16y^2\)[/tex] is [tex]\((4y)^2\)[/tex]
We can apply the difference of squares formula:
[tex]\[ 9x^2 - 16y^2 = (3x + 4y)(3x - 4y) \][/tex]
3. Combine Everything:
Now plug it back into the expression we factored the GCF out of:
[tex]\[ 27x^2 - 48y^2 = 3(3x + 4y)(3x - 4y) \][/tex]
So, the fully factored form of the expression [tex]\(27x^2 - 48y^2\)[/tex] is:
[tex]\[ 3(3x + 4y)(3x - 4y) \][/tex]
This solution involves recognizing the structure of the expression, identifying the difference of squares, and applying the appropriate factoring steps.
Thanks for taking the time to read Factor the expression 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
