Questions: Find the indicated product and express the result in simplest form. [ (sqrtx+5)^2 ]

Solution Steps

To find the indicated product and express the result in simplest form, we need to expand the expression \((\sqrt{x} + 5)^2\). This involves using the formula for the square of a binomial, \((a + b)^2 = a^2 + 2ab + b^2\), where \(a = \sqrt{x}\) and \(b = 5\).

We are given the expression \((\sqrt{x} + 5)^2\) and need to expand it.

To expand \((\sqrt{x} + 5)^2\), we use the formula for the square of a binomial: \[ (a + b)^2 = a^2 + 2ab + b^2 \] where \(a = \sqrt{x}\) and \(b = 5\).

• \(a^2 = (\sqrt{x})^2 = x\)
• \(2ab = 2 \cdot \sqrt{x} \cdot 5 = 10\sqrt{x}\)
• \(b^2 = 5^2 = 25\)

Combine the terms to get the expanded expression: \[ x + 10\sqrt{x} + 25 \]

Final Answer