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

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

where $ A = \color{blue}{ 2x } $ and $ B = \color{red}{ 3 }$.

$$ \begin{aligned}\left(2x+3\right)^2 = \color{blue}{\left( 2x \right)^2} +2 \cdot 2x \cdot 3 + \color{red}{3^2} = 4x^2+12x+9\end{aligned} $$

Find $ \left(x-2\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}{ 2 }$.

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

Multiply $ \color{blue}{2} $ by $ \left( x^2-4x+4\right) $ $$ \color{blue}{2} \cdot \left( x^2-4x+4\right) = 2x^2-8x+8 $$

Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x+1\right) $.

$$ \left( \color{blue}{x-1}\right) \cdot \left( x+1\right) = x^2+ \cancel{x} -\cancel{x}-1 $$

Combine like terms:

$$ x^2+ \, \color{blue}{ \cancel{x}} \, \, \color{blue}{ -\cancel{x}} \,-1 = x^2-1 $$

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

$$ - \left( 2x^2-8x+8 \right) = -2x^2+8x-8 $$

Combine like terms:

$$ \color{blue}{4x^2} + \color{red}{12x} + \color{green}{9} \color{blue}{-2x^2} + \color{red}{8x} \color{green}{-8} = \color{blue}{2x^2} + \color{red}{20x} + \color{green}{1} $$

Combine like terms:

$$ \color{blue}{2x^2} +20x+ \, \color{red}{ \cancel{1}} \,+ \color{blue}{x^2} \, \color{red}{ -\cancel{1}} \, = \color{blue}{3x^2} +20x $$