Find $ \left(x+7\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}{ 7 }$.

$$ \begin{aligned}\left(x+7\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 7 + \color{red}{7^2} = x^2+14x+49\end{aligned} $$

Multiply each term of $ \left( \color{blue}{x^2+14x+49}\right) $ by each term in $ \left( x+1\right) $.

$$ \left( \color{blue}{x^2+14x+49}\right) \cdot \left( x+1\right) = x^3+x^2+14x^2+14x+49x+49 $$

Combine like terms:

$$ x^3+ \color{blue}{x^2} + \color{blue}{14x^2} + \color{red}{14x} + \color{red}{49x} +49 = x^3+ \color{blue}{15x^2} + \color{red}{63x} +49 $$

Multiply each term of $ \left( \color{blue}{x^3+15x^2+63x+49}\right) $ by each term in $ \left( x-2\right) $.

$$ \left( \color{blue}{x^3+15x^2+63x+49}\right) \cdot \left( x-2\right) = x^4-2x^3+15x^3-30x^2+63x^2-126x+49x-98 $$

Combine like terms:

$$ x^4 \color{blue}{-2x^3} + \color{blue}{15x^3} \color{red}{-30x^2} + \color{red}{63x^2} \color{green}{-126x} + \color{green}{49x} -98 = x^4+ \color{blue}{13x^3} + \color{red}{33x^2} \color{green}{-77x} -98 $$

Multiply each term of $ \left( \color{blue}{x^4+13x^3+33x^2-77x-98}\right) $ by each term in $ \left( x-3\right) $.

$$ \left( \color{blue}{x^4+13x^3+33x^2-77x-98}\right) \cdot \left( x-3\right) = \\ = x^5-3x^4+13x^4-39x^3+33x^3-99x^2-77x^2+231x-98x+294 $$

Combine like terms:

$$ x^5 \color{blue}{-3x^4} + \color{blue}{13x^4} \color{red}{-39x^3} + \color{red}{33x^3} \color{green}{-99x^2} \color{green}{-77x^2} + \color{orange}{231x} \color{orange}{-98x} +294 = \\ = x^5+ \color{blue}{10x^4} \color{red}{-6x^3} \color{green}{-176x^2} + \color{orange}{133x} +294 $$