Answer
$$(b-7)(b+8)(3b-4)=3b^3-b^2-172b+224$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(b-7)(b+8)(3b-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1b^2+8b-7b-56)(3b-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1b^2+b-56)(3b-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3b^3-4b^2+3b^2-4b-168b+224 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3b^3-b^2-172b+224\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{b-7}\right) $ by each term in $ \left( b+8\right) $. $$ \left( \color{blue}{b-7}\right) \cdot \left( b+8\right) = b^2+8b-7b-56 $$ |
| ② | Combine like terms: $$ b^2+ \color{blue}{8b} \color{blue}{-7b} -56 = b^2+ \color{blue}{b} -56 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{b^2+b-56}\right) $ by each term in $ \left( 3b-4\right) $. $$ \left( \color{blue}{b^2+b-56}\right) \cdot \left( 3b-4\right) = 3b^3-4b^2+3b^2-4b-168b+224 $$ |
| ④ | Combine like terms: $$ 3b^3 \color{blue}{-4b^2} + \color{blue}{3b^2} \color{red}{-4b} \color{red}{-168b} +224 = 3b^3 \color{blue}{-b^2} \color{red}{-172b} +224 $$ |
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