Question

simplify. assume that all variables represent positive real numbers.
$(2\sqrt{x} - 3) (3\sqrt{x} + 2)$
\bigcirc $6x - 5\sqrt{x} - 6$
\bigcirc $\sqrt{x} - 6$
\bigcirc $6 - 5\sqrt{x}$
\bigcirc $6x - 2\sqrt{x} - 6$
\bigcirc $x - 6$

Explanation:

Step1: Apply FOIL method

Multiply the First terms: \(2\sqrt{x} \times 3\sqrt{x} = 6x\)
Multiply the Outer terms: \(2\sqrt{x} \times 2 = 4\sqrt{x}\)
Multiply the Inner terms: \(-3 \times 3\sqrt{x} = -9\sqrt{x}\)
Multiply the Last terms: \(-3 \times 2 = -6\)

Step2: Combine like terms

Combine the \(\sqrt{x}\) terms: \(4\sqrt{x} - 9\sqrt{x} = -5\sqrt{x}\)
Combine all terms: \(6x - 5\sqrt{x} - 6\)

Answer:

\(6x - 5\sqrt{x} - 6\) (corresponding to the first option: \(6x - 5\sqrt{x} - 6\))