Question

select the correct answer.

what is this expression in simplified form?

\\x^2 \sqrt{3} - 6x \sqrt{3} + x^2 \sqrt{48} - 4x\\

• \\(5x^2 \sqrt{3} - 10x \sqrt{3}\\)
• \\(-x^2 \sqrt{3} - 4x\\)
• \\(9x^2 \sqrt{3} - 6x \sqrt{3} - 4x\\)
• \\(5x^2 \sqrt{3} - 6x \sqrt{3} - 4x\\)

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Simplify the radical term

$$ x^2 \sqrt{48} = x^2 \sqrt{16 \cdot 3} = 4x^2 \sqrt{3} $$

Step 2: Rewrite the expression

$$ x^2 \sqrt{3} - 6x \sqrt{3} + 4x^2 \sqrt{3} - 4x $$

Step 3: Combine like terms

$$ (1x^2 \sqrt{3} + 4x^2 \sqrt{3}) - 6x \sqrt{3} - 4x = 5x^2 \sqrt{3} - 6x \sqrt{3} - 4x $$

Answer:

\( 5x^2 \sqrt{3} - 6x \sqrt{3} - 4x \) (the fourth option)