Question
Answer
$$(-3b-5)\cdot(5-3b)(m^2-n^3)(m^2+n^3)=-9b^2n^6+9b^2m^4+25n^6-25m^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-3b-5)\cdot(5-3b)(m^2-n^3)(m^2+n^3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-15b+9b^2-25+15b)(m^2-n^3)(m^2+n^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(9b^2-25)(m^2-n^3)(m^2+n^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(9b^2m^2-9b^2n^3-25m^2+25n^3)(m^2+n^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-9b^2n^6+9b^2m^4+25n^6-25m^4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-3b-5}\right) $ by each term in $ \left( 5-3b\right) $. $$ \left( \color{blue}{-3b-5}\right) \cdot \left( 5-3b\right) = -\cancel{15b}+9b^2-25+ \cancel{15b} $$ |
| ② | Combine like terms: $$ \, \color{blue}{ -\cancel{15b}} \,+9b^2-25+ \, \color{blue}{ \cancel{15b}} \, = 9b^2-25 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{9b^2-25}\right) $ by each term in $ \left( m^2-n^3\right) $. $$ \left( \color{blue}{9b^2-25}\right) \cdot \left( m^2-n^3\right) = 9b^2m^2-9b^2n^3-25m^2+25n^3 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{9b^2m^2-9b^2n^3-25m^2+25n^3}\right) $ by each term in $ \left( m^2+n^3\right) $. $$ \left( \color{blue}{9b^2m^2-9b^2n^3-25m^2+25n^3}\right) \cdot \left( m^2+n^3\right) = \\ = 9b^2m^4+ \cancel{9b^2m^2n^3} -\cancel{9b^2m^2n^3}-9b^2n^6-25m^4 -\cancel{25m^2n^3}+ \cancel{25m^2n^3}+25n^6 $$ |
| ⑤ | Combine like terms: $$ 9b^2m^4+ \, \color{blue}{ \cancel{9b^2m^2n^3}} \, \, \color{blue}{ -\cancel{9b^2m^2n^3}} \,-9b^2n^6-25m^4 \, \color{green}{ -\cancel{25m^2n^3}} \,+ \, \color{green}{ \cancel{25m^2n^3}} \,+25n^6 = -9b^2n^6+9b^2m^4+25n^6-25m^4 $$ |
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