Question
Answer
$$(5s^2-9s)x(3t^2+t)(2x+5)=30s^2t^2x^2+75s^2t^2x+10s^2tx^2-54st^2x^2+25s^2tx-135st^2x-18stx^2-45stx$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5s^2-9s)x(3t^2+t)(2x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(5s^2x-9sx)(3t^2+t)(2x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(15s^2t^2x+5s^2tx-27st^2x-9stx)(2x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}30s^2t^2x^2+75s^2t^2x+10s^2tx^2-54st^2x^2+25s^2tx-135st^2x-18stx^2-45stx\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{5s^2-9s}\right) \cdot x = 5s^2x-9sx $$ |
| ② | Multiply each term of $ \left( \color{blue}{5s^2x-9sx}\right) $ by each term in $ \left( 3t^2+t\right) $. $$ \left( \color{blue}{5s^2x-9sx}\right) \cdot \left( 3t^2+t\right) = 15s^2t^2x+5s^2tx-27st^2x-9stx $$ |
| ③ | Multiply each term of $ \left( \color{blue}{15s^2t^2x+5s^2tx-27st^2x-9stx}\right) $ by each term in $ \left( 2x+5\right) $. $$ \left( \color{blue}{15s^2t^2x+5s^2tx-27st^2x-9stx}\right) \cdot \left( 2x+5\right) = \\ = 30s^2t^2x^2+75s^2t^2x+10s^2tx^2+25s^2tx-54st^2x^2-135st^2x-18stx^2-45stx $$ |
| ④ | Combine like terms: $$ 30s^2t^2x^2+75s^2t^2x+10s^2tx^2+25s^2tx-54st^2x^2-135st^2x-18stx^2-45stx = \\ = 30s^2t^2x^2+75s^2t^2x+10s^2tx^2-54st^2x^2+25s^2tx-135st^2x-18stx^2-45stx $$ |
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