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 }$.

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

Find $ \left(x+1\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}{ 1 }$.

$$ \begin{aligned}\left(x+1\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 1 + \color{red}{1^2} = x^2+2x+1\end{aligned} $$

Multiply $ \color{blue}{2} $ by $ \left( x^2+2x+1\right) $ $$ \color{blue}{2} \cdot \left( x^2+2x+1\right) = 2x^2+4x+2 $$Multiply $ \color{blue}{2} $ by $ \left( x+1\right) $ $$ \color{blue}{2} \cdot \left( x+1\right) = 2x+2 $$

Combine like terms:

$$ 2x^2+ \color{blue}{4x} + \color{red}{2} + \color{blue}{2x} + \color{red}{2} = 2x^2+ \color{blue}{6x} + \color{red}{4} $$

Combine like terms:

$$ 2x^2+6x+ \color{blue}{4} \color{blue}{-1} = 2x^2+6x+ \color{blue}{3} $$

Multiply each term of $ \left( \color{blue}{x^2+4x+4}\right) $ by each term in $ \left( 2x^2+6x+3\right) $.

$$ \left( \color{blue}{x^2+4x+4}\right) \cdot \left( 2x^2+6x+3\right) = 2x^4+6x^3+3x^2+8x^3+24x^2+12x+8x^2+24x+12 $$

Combine like terms:

$$ 2x^4+ \color{blue}{6x^3} + \color{red}{3x^2} + \color{blue}{8x^3} + \color{green}{24x^2} + \color{orange}{12x} + \color{green}{8x^2} + \color{orange}{24x} +12 = \\ = 2x^4+ \color{blue}{14x^3} + \color{green}{35x^2} + \color{orange}{36x} +12 $$