# How do you simplify (2+sqrtx)(8+sqrtx)?

Jan 23, 2017

$16 + 10 \sqrt{x} + x$

#### Explanation:

Each term in the second bracket must be multiplied by each term in the first bracket. This can be achieved as follows.

$\Rightarrow \left(\textcolor{red}{2 + \sqrt{x}}\right) \left(8 + \sqrt{x}\right)$

$= \textcolor{red}{2} \left(8 + \sqrt{x}\right) \textcolor{red}{+ \sqrt{x}} \left(8 + \sqrt{x}\right)$

distribute the brackets.

$\Rightarrow 16 + 2 \sqrt{x} + 8 \sqrt{x} + \left(\sqrt{x} \times \sqrt{x}\right)$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\sqrt{x} \times \sqrt{x} = x} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

collecting like terms and simplifying.

$= 16 + 10 \sqrt{x} + x$