Answer
$$(x+3)(x+75)^2=x^3+153x^2+6075x+16875$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+3)(x+75)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x+3)(x^2+150x+5625) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3+150x^2+5625x+3x^2+450x+16875 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+153x^2+6075x+16875\end{aligned} $$ | |
| ① | Find $ \left(x+75\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}{ 75 }$. $$ \begin{aligned}\left(x+75\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 75 + \color{red}{75^2} = x^2+150x+5625\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x+3}\right) $ by each term in $ \left( x^2+150x+5625\right) $. $$ \left( \color{blue}{x+3}\right) \cdot \left( x^2+150x+5625\right) = x^3+150x^2+5625x+3x^2+450x+16875 $$ |
| ③ | Combine like terms: $$ x^3+ \color{blue}{150x^2} + \color{red}{5625x} + \color{blue}{3x^2} + \color{red}{450x} +16875 = x^3+ \color{blue}{153x^2} + \color{red}{6075x} +16875 $$ |
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