Question
Answer
$$3(2x-5)(x^2-4x+2)=6x^3-39x^2+72x-30$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(2x-5)(x^2-4x+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6x-15)(x^2-4x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6x^3-24x^2+12x-15x^2+60x-30 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x^3-39x^2+72x-30\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 2x-5\right) $ $$ \color{blue}{3} \cdot \left( 2x-5\right) = 6x-15 $$ |
| ② | Multiply each term of $ \left( \color{blue}{6x-15}\right) $ by each term in $ \left( x^2-4x+2\right) $. $$ \left( \color{blue}{6x-15}\right) \cdot \left( x^2-4x+2\right) = 6x^3-24x^2+12x-15x^2+60x-30 $$ |
| ③ | Combine like terms: $$ 6x^3 \color{blue}{-24x^2} + \color{red}{12x} \color{blue}{-15x^2} + \color{red}{60x} -30 = 6x^3 \color{blue}{-39x^2} + \color{red}{72x} -30 $$ |
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