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)^3 $ using formula

$$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$

where $ A = x $ and $ B = 2h $.

$$ \left(x+2h\right)^3 = x^3+3 \cdot x^2 \cdot 2h + 3 \cdot x \cdot \left( 2h \right)^2+\left( 2h \right)^3 = x^3+6hx^2+12h^2x+8h^3 $$

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

$$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$

where $ A = x $ and $ B = h $.

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

Multiply $ \color{blue}{3} $ by $ \left( x^3+6hx^2+12h^2x+8h^3\right) $ $$ \color{blue}{3} \cdot \left( x^3+6hx^2+12h^2x+8h^3\right) = 3x^3+18hx^2+36h^2x+24h^3 $$Multiply $ \color{blue}{3} $ by $ \left( x^3+3hx^2+3h^2x+h^3\right) $ $$ \color{blue}{3} \cdot \left( x^3+3hx^2+3h^2x+h^3\right) = 3x^3+9hx^2+9h^2x+3h^3 $$

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

$$ - \left( 3x^3+18hx^2+36h^2x+24h^3 \right) = -3x^3-18hx^2-36h^2x-24h^3 $$

Combine like terms:

$$ x^2+6hx+9h^2 \, \color{blue}{ -\cancel{3x^3}} \, \color{green}{-18hx^2} \color{orange}{-36h^2x} \color{blue}{-24h^3} + \, \color{blue}{ \cancel{3x^3}} \,+ \color{green}{9hx^2} + \color{orange}{9h^2x} + \color{blue}{3h^3} = \\ = \color{blue}{-21h^3} \color{orange}{-27h^2x} \color{green}{-9hx^2} +9h^2+6hx+x^2 $$

Combine like terms:

$$ -21h^3-27h^2x-9hx^2-x^3+9h^2+6hx+x^2 = -21h^3-27h^2x-9hx^2-x^3+9h^2+6hx+x^2 $$