Answer
$$2b(4b-7)(3b+2)-b(5b+2)(b-6)=19b^3+2b^2-16b$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2b(4b-7)(3b+2)-b(5b+2)(b-6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(8b^2-14b)(3b+2)-(5b^2+2b)(b-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}24b^3+16b^2-42b^2-28b-(5b^3-30b^2+2b^2-12b) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}24b^3-26b^2-28b-(5b^3-28b^2-12b) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}24b^3-26b^2-28b-5b^3+28b^2+12b \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}19b^3+2b^2-16b\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2b} $ by $ \left( 4b-7\right) $ $$ \color{blue}{2b} \cdot \left( 4b-7\right) = 8b^2-14b $$Multiply $ \color{blue}{b} $ by $ \left( 5b+2\right) $ $$ \color{blue}{b} \cdot \left( 5b+2\right) = 5b^2+2b $$ |
| ② | Multiply each term of $ \left( \color{blue}{8b^2-14b}\right) $ by each term in $ \left( 3b+2\right) $. $$ \left( \color{blue}{8b^2-14b}\right) \cdot \left( 3b+2\right) = 24b^3+16b^2-42b^2-28b $$Multiply each term of $ \left( \color{blue}{5b^2+2b}\right) $ by each term in $ \left( b-6\right) $. $$ \left( \color{blue}{5b^2+2b}\right) \cdot \left( b-6\right) = 5b^3-30b^2+2b^2-12b $$ |
| ③ | Combine like terms: $$ 24b^3+ \color{blue}{16b^2} \color{blue}{-42b^2} -28b = 24b^3 \color{blue}{-26b^2} -28b $$Combine like terms: $$ 5b^3 \color{blue}{-30b^2} + \color{blue}{2b^2} -12b = 5b^3 \color{blue}{-28b^2} -12b $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 5b^3-28b^2-12b \right) = -5b^3+28b^2+12b $$ |
| ⑤ | Combine like terms: $$ \color{blue}{24b^3} \color{red}{-26b^2} \color{green}{-28b} \color{blue}{-5b^3} + \color{red}{28b^2} + \color{green}{12b} = \color{blue}{19b^3} + \color{red}{2b^2} \color{green}{-16b} $$ |
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