Question

Simplify the expression. $$(\sqrt{c}+d)(3+\sqrt{5})$$

Short answer

The simplified version of the expression \((\sqrt{c}+d)(3+\sqrt{5})\) is \(3\sqrt{c} + \sqrt{5c} + 3d + d\sqrt{5}\).

Step-by-step solution

- Distribute the first terms

Multiply the first term in the first bracket with all terms in the second bracket: \((\sqrt{c})(3) + (\sqrt{c})(\sqrt{5})\)

- Distribute the second terms

Multiply the second term in the first bracket with all terms in the second bracket: \((d)(3) + (d)(\sqrt{5})\)

- Combine like terms

Regroup the expression by combined like terms: \(3\sqrt{c} + \sqrt{5c} + 3d + d\sqrt{5}\)

- Simplify the expression

The expression is simplified as much as possible. The final expression is \(3\sqrt{c} + \sqrt{5c} + 3d + d\sqrt{5}\).