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}{3} $ by $ \left( 4x-5\right) $ $$ \color{blue}{3} \cdot \left( 4x-5\right) = 12x-15 $$

Multiply each term of $ \left( \color{blue}{12x-15}\right) $ by each term in $ \left( x^2+2x+1\right) $.

$$ \left( \color{blue}{12x-15}\right) \cdot \left( x^2+2x+1\right) = 12x^3+24x^2+12x-15x^2-30x-15 $$

Combine like terms:

$$ 12x^3+ \color{blue}{24x^2} + \color{red}{12x} \color{blue}{-15x^2} \color{red}{-30x} -15 = 12x^3+ \color{blue}{9x^2} \color{red}{-18x} -15 $$

Multiply each term of $ \left( \color{blue}{12x^3+9x^2-18x-15}\right) $ by each term in $ \left( 3x+2\right) $.

$$ \left( \color{blue}{12x^3+9x^2-18x-15}\right) \cdot \left( 3x+2\right) = 36x^4+24x^3+27x^3+18x^2-54x^2-36x-45x-30 $$

Combine like terms:

$$ 36x^4+ \color{blue}{24x^3} + \color{blue}{27x^3} + \color{red}{18x^2} \color{red}{-54x^2} \color{green}{-36x} \color{green}{-45x} -30 = \\ = 36x^4+ \color{blue}{51x^3} \color{red}{-36x^2} \color{green}{-81x} -30 $$