Question
Answer
$$(-45n^2+30nx-5x^2+15n+5)(3n-x)=-135n^3+135n^2x-45nx^2+5x^3+45n^2-15nx+15n-5x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-45n^2+30nx-5x^2+15n+5)(3n-x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-135n^3+135n^2x-45nx^2+5x^3+45n^2-15nx+15n-5x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-45n^2+30nx-5x^2+15n+5}\right) $ by each term in $ \left( 3n-x\right) $. $$ \left( \color{blue}{-45n^2+30nx-5x^2+15n+5}\right) \cdot \left( 3n-x\right) = \\ = -135n^3+45n^2x+90n^2x-30nx^2-15nx^2+5x^3+45n^2-15nx+15n-5x $$ |
| ② | Combine like terms: $$ -135n^3+ \color{blue}{45n^2x} + \color{blue}{90n^2x} \color{red}{-30nx^2} \color{red}{-15nx^2} +5x^3+45n^2-15nx+15n-5x = \\ = -135n^3+ \color{blue}{135n^2x} \color{red}{-45nx^2} +5x^3+45n^2-15nx+15n-5x $$ |
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