# How do you simplify (4sqrtx+1)(3sqrtx+2)?

May 18, 2017

See a solution process below:

#### Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

(color(red)(4sqrt(x)) + color(red)(1))(color(blue)(3sqrt(x) + color(blue)(2)) becomes:

$\left(\textcolor{red}{4 \sqrt{x}} \times \textcolor{b l u e}{3 \sqrt{x}}\right) + \left(\textcolor{red}{4 \sqrt{x}} \times \textcolor{b l u e}{2}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{3 \sqrt{x}}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{2}\right)$

$12 {\left(\sqrt{x}\right)}^{2} + 8 \sqrt{x} + 3 \sqrt{x} + 2$

$12 x + 8 \sqrt{x} + 3 \sqrt{x} + 2$

We can now combine like terms:

$12 x + \left(8 + 3\right) \sqrt{x} + 2$

$12 x + 11 \sqrt{x} + 2$