Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Certainly! Let's expand and simplify the given expression step by step:
We need to simplify the expression [tex]\((\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3})\)[/tex].
1. Recognize the Structure:
The expression [tex]\((\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3})\)[/tex] is in the form of a difference of squares, which can be represented as:
[tex]\[ (a + b)(a - b) = a^2 - b^2 \][/tex]
2. Identify [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
Here, [tex]\(a = \sqrt{6}\)[/tex] and [tex]\(b = \sqrt{3}\)[/tex].
3. Apply the Formula:
We apply the difference of squares formula:
[tex]\[ (\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3}) = (\sqrt{6})^2 - (\sqrt{3})^2 \][/tex]
4. Calculate Each Term:
- Calculate [tex]\((\sqrt{6})^2\)[/tex]:
[tex]\[ (\sqrt{6})^2 = 6 \][/tex]
- Calculate [tex]\((\sqrt{3})^2\)[/tex]:
[tex]\[ (\sqrt{3})^2 = 3 \][/tex]
5. Subtract the Results:
Now, subtract the second term from the first:
[tex]\[ 6 - 3 = 3 \][/tex]
6. Conclusion:
Therefore, the simplified form of [tex]\((\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3})\)[/tex] is:
[tex]\[ 3 \][/tex]
So, [tex]\((\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3}) = 3\)[/tex].
We need to simplify the expression [tex]\((\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3})\)[/tex].
1. Recognize the Structure:
The expression [tex]\((\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3})\)[/tex] is in the form of a difference of squares, which can be represented as:
[tex]\[ (a + b)(a - b) = a^2 - b^2 \][/tex]
2. Identify [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
Here, [tex]\(a = \sqrt{6}\)[/tex] and [tex]\(b = \sqrt{3}\)[/tex].
3. Apply the Formula:
We apply the difference of squares formula:
[tex]\[ (\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3}) = (\sqrt{6})^2 - (\sqrt{3})^2 \][/tex]
4. Calculate Each Term:
- Calculate [tex]\((\sqrt{6})^2\)[/tex]:
[tex]\[ (\sqrt{6})^2 = 6 \][/tex]
- Calculate [tex]\((\sqrt{3})^2\)[/tex]:
[tex]\[ (\sqrt{3})^2 = 3 \][/tex]
5. Subtract the Results:
Now, subtract the second term from the first:
[tex]\[ 6 - 3 = 3 \][/tex]
6. Conclusion:
Therefore, the simplified form of [tex]\((\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3})\)[/tex] is:
[tex]\[ 3 \][/tex]
So, [tex]\((\sqrt{6} + \sqrt{3})(\sqrt{6} - \sqrt{3}) = 3\)[/tex].
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.