simplify: $(-\sqrt{x-4})^2$

$\bigcirc$ $-x+4$
$\bigcirc$ $x-4$
$\bigcirc$ $2x-8$

Question

simplify: $(-\sqrt{x-4})^2$

$\bigcirc$ $-x+4$
$\bigcirc$ $x-4$
$\bigcirc$ $2x-8$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Algebraic Simplification" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Algebraic Simplification", "Radical Expressions" ] } ## Apply the power of a product rule Using the *Exponent Rules* knowledge point $$ (-\sqrt{x-4})^2 = (-1)^2 \cdot (\sqrt{x-4})^2 $$ ## Simplify the squared terms Using the *Algebraic Simplification* knowledge point $$ \begin{aligned} (-1)^2 &= 1 \ (\sqrt{x-4})^2 &= x - 4 \quad (\text{for } x \ge 4) \ (-\sqrt{x-4})^2 &= 1 \cdot (x - 4) = x - 4 \end{aligned} $$

-x + 4

x - 4

2x - 8

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the power of a product rule

Simplify the squared terms

Answer: