Question

multiply. assume that all variables represent positive real numbers.
$(6\sqrt{x} + 8)(5\sqrt{x} - 2)$

$(6\sqrt{x} + 8)(5\sqrt{x} - 2) = \square$
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply the First terms: \(6\sqrt{x} \times 5\sqrt{x} = 30x\) (since \(\sqrt{x} \times \sqrt{x} = x\))
Multiply the Outer terms: \(6\sqrt{x} \times (-2) = -12\sqrt{x}\)
Multiply the Inner terms: \(8 \times 5\sqrt{x} = 40\sqrt{x}\)
Multiply the Last terms: \(8 \times (-2) = -16\)

Step2: Combine like terms

Combine the radical terms: \(-12\sqrt{x} + 40\sqrt{x} = 28\sqrt{x}\)
Combine the constant and the \(x\) term: \(30x - 16\)

Step3: Write the final expression

Combine all terms: \(30x + 28\sqrt{x} - 16\)

Answer:

\(30x + 28\sqrt{x} - 16\)