Question

multiply. assume that all variables represent positive real numbers.
$(6\sqrt{x} + 7)(2\sqrt{x} + 9)$

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply the First terms: \(6\sqrt{x} \times 2\sqrt{x} = 12x\)
Multiply the Outer terms: \(6\sqrt{x} \times 9 = 54\sqrt{x}\)
Multiply the Inner terms: \(7 \times 2\sqrt{x} = 14\sqrt{x}\)
Multiply the Last terms: \(7 \times 9 = 63\)

Step2: Combine like terms

Combine the terms with \(\sqrt{x}\): \(54\sqrt{x} + 14\sqrt{x} = 68\sqrt{x}\)

Step3: Combine all terms

Add the results from Step1 and Step2: \(12x + 68\sqrt{x} + 63\)

Answer:

\(12x + 68\sqrt{x} + 63\)