multiply and simplify.

\(\sqrt{x} + 3\sqrt{2})^2 = \
\(\sqrt{x} - \sqrt{2})(\sqrt{x} + \sqrt{2}) = \

Question

multiply and simplify.

\(\sqrt{x} + 3\sqrt{2})^2 = \
\(\sqrt{x} - \sqrt{2})(\sqrt{x} + \sqrt{2}) = \

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Multiplication", "Distributive Property", "Radical Simplification" ], "new_concepts": [], "current_concepts": [ "Radical Multiplication", "Distributive Property", "Radical Simplification", "Algebraic Identities" ] } ## Expand the first expression using binomial square identity $$ \begin{aligned} (\sqrt{x} + 3\sqrt{2})^2 &= (\sqrt{x})^2 + 2(\sqrt{x})(3\sqrt{2}) + (3\sqrt{2})^2 \ &= x + 6\sqrt{2x} + 9(2) \ &= x + 6\sqrt{2x} + 18 \end{aligned} $$ ## Expand the second expression using difference of squares identity $$ \begin{aligned} (\sqrt{x} - \sqrt{2})(\sqrt{x} + \sqrt{2}) &= (\sqrt{x})^2 - (\sqrt{2})^2 \ &= x - 2 \end{aligned} $$ ## Question 1 $(\sqrt{x} + 3\sqrt{2})^2 =$ $x + 6\sqrt{2x} + 18$ ## Question 2 $(\sqrt{x} - \sqrt{2})(\sqrt{x} + \sqrt{2}) =$ $x - 2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Expressions and Algebraic Identities" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the first expression using binomial square identity

Expand the second expression using difference of squares identity

Answer:

Question 1

Question 2