# How do you simplify 2(sqrt(5x) - 3)^2?

$10 x - 12 \sqrt{5 x} + 18$

#### Explanation:

We can rewrite the expression to specifically show all the terms:

$2 {\left(\sqrt{5 x} - 3\right)}^{2} = 2 \left(\sqrt{5 x} - 3\right) \left(\sqrt{5 x} - 3\right)$

Let's set aside the leading 2 for a minute and work with the two bracketed terms. We'll use FOIL to handle it:

FOIL

• $\textcolor{red}{F}$ - First terms - $\left(\textcolor{red}{a} + b\right) \left(\textcolor{red}{c} + d\right)$
• $\textcolor{b r o w n}{O}$ - Outside terms - $\left(\textcolor{b r o w n}{a} + b\right) \left(c + \textcolor{b r o w n}{d}\right)$
• $\textcolor{b l u e}{I}$ - Inside terms - $\left(a + \textcolor{b l u e}{b}\right) \left(\textcolor{b l u e}{c} + d\right)$
• $\textcolor{g r e e n}{L}$ - Last terms - $\left(a + \textcolor{g r e e n}{b}\right) \left(c + \textcolor{g r e e n}{d}\right)$

This gives us:

• $\textcolor{red}{F} \implies \sqrt{5 x} \sqrt{5 x} = 5 x$
• $\textcolor{b r o w n}{O} \implies \sqrt{5 x} \left(- 3\right) = - 3 \sqrt{5 x}$
• $\textcolor{b l u e}{I} \implies \left(- 3\right) \left(\sqrt{5 x}\right) = - 3 \sqrt{5 x}$
• $\textcolor{g r e e n}{L} \implies \left(- 3\right) \left(- 3\right) = 9$

$5 x - 3 \sqrt{5 x} - 3 \sqrt{5 x} + 9 = 5 x - 6 \sqrt{5 x} + 9$

And so $2 {\left(\sqrt{5 x} - 3\right)}^{2} = 2 \left(5 x - 6 \sqrt{5 x} + 9\right)$

We can now distribute the 2 through the bracket:

2(5x-6sqrt(5x)+9)=color(blue)(ul(bar(abs(color(black)(10x-12sqrt(5x)+18))))