Find $ \left(x+3h\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 3h }$.

$$ \begin{aligned}\left(x+3h\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 3h + \color{red}{\left( 3h \right)^2} = x^2+6hx+9h^2\end{aligned} $$

Find $ \left(x+2h\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2h }$.

$$ \begin{aligned}\left(x+2h\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2h + \color{red}{\left( 2h \right)^2} = x^2+4hx+4h^2\end{aligned} $$

Find $ \left(x+h\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ x } $ and $ B = \color{red}{ h }$.

$$ \begin{aligned}\left(x+h\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot h + \color{red}{h^2} = x^2+2hx+h^2\end{aligned} $$

Multiply $ \color{blue}{3} $ by $ \left( x^2+4hx+4h^2\right) $ $$ \color{blue}{3} \cdot \left( x^2+4hx+4h^2\right) = 3x^2+12hx+12h^2 $$Multiply $ \color{blue}{3} $ by $ \left( x^2+2hx+h^2\right) $ $$ \color{blue}{3} \cdot \left( x^2+2hx+h^2\right) = 3x^2+6hx+3h^2 $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( 3x^2+12hx+12h^2 \right) = -3x^2-12hx-12h^2 $$

Combine like terms:

$$ \color{blue}{x^2} + \color{red}{6hx} + \color{green}{9h^2} \color{blue}{-3x^2} \color{red}{-12hx} \color{green}{-12h^2} = \color{green}{-3h^2} \color{red}{-6hx} \color{blue}{-2x^2} $$

Combine like terms:

$$ \, \color{blue}{ -\cancel{3h^2}} \, \, \color{green}{ -\cancel{6hx}} \, \color{blue}{-2x^2} + \color{blue}{3x^2} + \, \color{green}{ \cancel{6hx}} \,+ \, \color{blue}{ \cancel{3h^2}} \, = \color{blue}{x^2} $$

Combine like terms:

$$ \, \color{blue}{ \cancel{x^2}} \, \, \color{blue}{ -\cancel{x^2}} \, = 0 $$