Math Problem Statement
Expand the expression \(\left(3 \sqrt{x} + \sqrt{2}\right)^2\).
Solution
The expression provided is:
To expand this, we can apply the formula for the square of a binomial , where:
Step-by-Step Solution:
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Square the first term:
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Multiply the two terms together and double the result:
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Square the second term:
Putting It All Together:
Combining all terms, we get:
Would you like further details on any part of this expansion?
Related Questions:
- What is the general formula for expanding ?
- How do we simplify terms involving square roots?
- What happens if in this expression?
- How can we factor expressions involving square roots?
- How would the expression change if we had ?
Tip:
When expanding binomials with square roots, keep each square root in its own term until you can combine terms. This minimizes errors in simplification.
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Math Problem Analysis
Mathematical Concepts
Algebra
Binomial Expansion
Square Roots
Formulas
Square of a binomial: \((a + b)^2 = a^2 + 2ab + b^2\)
Theorems
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Suitable Grade Level
Grades 9-10