Q. 591 - Intermediate Algebra

Question

In the following exercises, simplify. Assume all variables are positive.

$\left(4-3\sqrt{3}\right)\left(5+2\sqrt{3}\right)$

Step-by-Step Solution

Answer

The simplified expression is $2-7\sqrt{3}.$

Step 1. Given Information

We have $\left(4-3\sqrt{3}\right)\left(5+2\sqrt{3}\right)$

Step 2. Simplify by distributive property

$$\begin{gathered} \left(4-3\sqrt{3}\right)\left(5+2\sqrt{3}\right) \\ =20+8\sqrt{3}-15\sqrt{3}-6\times 3 \\ =20-7\sqrt{3}-18 \\ =2-7\sqrt{3} \end{gathered}$$